Gentry, who was fired by the Pelicans in August after the team missed the playoffs for a second straight season, reunites with Kings head coach Luke Walton.
The pair were assistants under Steve Kerr with Golden State during the 2014-15 campaign, a season in which the Warriors won an NBA-best 67 games and defeated the Cleveland Cavaliers in the NBA Finals.
The 65-year-old Gentry brings 17 years of experience as an NBA head coach to Sacramento, the last five coming with New Orleans. He also served in that role with Miami (1995), Detroit (1997-2000), the Los Angeles Clippers (2000-03) and Phoenix (2008-13).
"I'm excited to add Alvin's valuable experience and leadership to the team," said Walton. "His veteran coaching perspective will be a great addition and I looking forward to working with him again to continue developing our group."
Gentry has compiled a 510-595 overall record as a head coach, including a 175-225 mark with the Pelicans. His best season came with the Suns in 2009-10, when Phoenix won 54 regular season games and reached the Western Conference Finals while leading the NBA in scoring at 110.2 points per game.
Sacramento finished 31-41 in Walton's first season in 2019-20. The Kings have missed the playoffs in 14 consecutive seasons, the longest active streak in the NBA.
The comments came after the Serbian scored 38 points in a 106-100 win for the Denver Nuggets on Wednesday, helping Michael Malone's men to their fourth consecutive victory.
The reigning MVP posted 32 points against the Golden State Warriors and 46 against the New Orleans Pelicans in the Nuggets' previous two outings. He is the first NBA player to average 35 or more points, 15 or more rebounds and 10 or more assists over a three-game run since Wilt Chamberlain did so between March 16-19, 1968.
After seeing Sacramento dominated by the 27-year-old, Gentry said he deserved a second consecutive MVP prize.
"That guy is just a different beast," he said post-game.
"He doesn't get shaken, he just does what he needs to do to win the game.
"He's just playing at such a high level, 46 points, 32 points, 38 tonight, he's just a different guy.
"Watching him play, it's hard to believe he won't be the MVP.
"He's playing at such a high level and does so many things on the court, I think he's one of those guys you could take and put on any team, and that team's going to be pretty successful."
Denver have now won 12 of their past 14 games, while Jokic fell just three assists short of registering a third consecutive triple-double.
His average of 25.9 points per game, meanwhile, is the ninth-strongest record among NBA players this season.
Jokic himself was pleased after recording another dominating performance in Sacramento but was keen to look ahead, with the Nuggets facing a rematch with the Warriors next on Thursday.
"Lately, we're playing really good, we're winning games," said the 27-year-old.
"Hopefully, it's going to continue."
Gentry was appointed on a temporary basis in November after Luke Walton was dismissed following a 6-11 start to the season.
The Kings went 24-41 under the former New Orleans Pelicans coach and finished 12th in the Western Conference, missing the playoffs for a 16th straight season.
It was confirmed on Monday that Gentry would not return to the Kings for the 2022-23 campaign.
General manager Monte McNair said in a statement: "The entire Kings organisation is grateful for the leadership of Alvin Gentry, who stepped up when he got the call mid-season.
"We appreciate his leadership on and off the court."
Gentry, who had been in charge since May 2015, guided the Pelicans to a 30-42 season in 2019-20, enough only for 13th place in the West.
New Orleans vice president of basketball operations David Griffin said on Saturday: "I'm grateful for and appreciative of Alvin's commitment to the organisation and, most importantly, the local community. The city of New Orleans is richer because of his presence here.
"These types of moves are often about fit and timing, and we believe now is the right time to make this change and bring in a new voice."
Owner Gayle Benson added: "Our intention moving forward is to find the right head coach that will guide this Pelicans team to compete for championships. That is what our fans deserve."
Big things were expected of the Pelicans this year after they landed the number one pick in the 2019 draft lottery and selected standout Duke star Zion Williamson.
Williamson tore his meniscus in preseason, however, and could not make his professional debut until January, by which point New Orleans were struggling to stay in the postseason picture.
Improved displays with the rookie in the team did enough to at least secure an invite to the Orlando 'bubble' amid the coronavirus pandemic, playing eight seeding games.
But Gentry's Pelicans finished last among those Western Conference teams to make the trip to Florida - despite a relatively kind schedule - with Williamson again struggling for fitness after leaving the 'bubble' ahead of the restart before returning.
It was a familiar disappointing theme for New Orleans, who only reached the playoffs in one of Gentry's five seasons at the helm.
Led by Anthony Davis, who made a blockbuster trade to the Los Angeles Lakers last year, the team lost in the conference semi-finals in 2017-18.
The number one overall draft pick belatedly made his regular-season bow following knee surgery, scoring 22 points - including 17 in a stunning fourth-quarter stretch - in the 121-117 defeat to the San Antonio Spurs.
Williamson made each of his four three-pointers following a slow start, and head coach Gentry quickly saw progress in his game.
"I think you'll see that in him," Gentry said. "It's his first NBA game, but I think the third time he went out there he was much more comfortable, much more aggressive.
"He found out that everybody makes mistakes and he just continued to play through them. I think, for him, it was just a relief to have one game under his belt.
"And now all of this goes away: first game, first game, first game. Now he can just play and get himself in a situation where he can continue to learn and continue to grow."
Gentry saw evidence of Williamson's "really, really high ceiling" but had to take the 19-year-old out of the game with more than five minutes left on doctors' orders.
"It was going to be a learning experience either way - if he played well, if he didn't play well," the coach said.
"I think the big thing is that he was much more aggressive during that situation. We talked at half-time, as I thought he was deferring way too much and I wanted him to be aggressive.
"I knew that he would make some mistakes, but I think what you saw there is a taste of what [is to come]. Once we get settled in and he gets settled in, there are a lot of things that we can do with him.
"There's a lot of potential there. It was good to see him do that. But I think there's a really, really high ceiling that he can reach. We'll just continue on, continue to practice.
"And no, he couldn't go back in the game. So don't go there. The medical people said that was it.
"We've got to be smart about it. I'm pretty sure Sean [Payton, New Orleans Saints coach] wouldn't take Drew Brees out in that situation. But we've got to be smart about it.
"We have to look long term and not one game, short term, and put him out there extended minutes. We were not going to do that in any situation.
"I think he made his point and he will continue to get better. But we can't sacrifice his whole future for one short-term thing."
Team-mate Holiday is certainly excited about what is to come, appearing alongside Williamson at a post-game news conference and interrupting one question to explain there is no return to "normal" when it comes to the teenager.
"This is going to be normal for him," Holiday said. "The way he plays, this is something he could do every day.
"We're here to help him and obviously for him to contribute to us and help us out, too. But with him being back, he's waited a long time for this and he's really excited to play - speaking for Zion."
The 2019-20 NBA season restarted on Thursday with a 22-team tournament in Orlando and the Pelicans' defeat left them 4.5 games back from the eighth seed – and the final playoff spot – in the Western Conference with seven to play.
They were leading by four points when Williamson exited midway through the fourth quarter and the rookie sensation – who scored 13 points in 15 minutes – did not return down the stretch.
Williamson, whose much-anticipated debut campaign in the NBA was delayed until January by a knee injury, had to leave the NBA's 'bubble' in Orlando to attend to an "urgent family matter", only returning last Friday, at which point he had to quarantine for four days.
"Of course, we wish we could've played him down the stretch, but we used the minutes that were given to us and that's the way it is," coach Gentry said, according to ESPN.
"We weren't going to stick him back out there. The medical people said we played them in the minutes that were allowed for us to play him, and just move on.
"I thought he looked good, I thought he had some good moments, and obviously we're a much better and different team when he's out on the floor.
"I was told the minutes that he could play, and that's what I did."
Williamson, who missed the first 43 games of the season following knee surgery, explained that it was a case of finding his rhythm again as he went 6-for-8 shooting.
The rookie said: "They weren't holding me back.
"Yeah, I did want to be out there, but we're just working my way back into my flow. That's all it is."
