The 2019 first-round pick faced competition from veteran Alex Smith - who is coming back from a horrific leg injury - and the recently acquired Kyle Allen, who is well known to Rivera following their time with the Carolina Panthers.
After a difficult season in 2019, Haskins has been given the full backing of his new coach.
"Dwayne's lived up to everything we talked about in January," Rivera said. "He deserves the opportunity. He's going to get the opportunity, and he's going to get my support."
Meanwhile, the Los Angeles Chargers have named Tyrod Taylor their starting quarterback for 2020.
The 31-year-old, who was the Buffalo Bills' starter from 2015 to 2017, has been preferred to rookie Justin Herbert for the spot.
"Right now Tyrod Taylor is our starter," Chargers coach Anthony Lynn said.
"Until someone steps up and shows that they can run this team, that's the way we're going into it."
The Chargers open their 2020 season at the Cincinnati Bengals on September 13, the same day that Washington take on Philadelphia.
Texans head coach David Culley announced on Tuesday that 32-year-old Taylor will not face the Panthers, having suffered the injury in the 31-21 loss to the Cleveland Browns in Week 2.
Taylor will be placed on injured reserve, meaning he will miss three weeks at a minimum.
Culley said veteran Jeff Driskel may be called up to back up 22-year-old Mills, who was a third-round pick in the 2021 Draft.
"He is ready," Culley said about Mills, who came off the bench against the Browns. "He's been exactly what you want your backup quarterback to be."
Mills went eight from 18 for 102 yards, including one touchdown pass against the Browns.
"When he went in the game this past week it had nothing to do with other than the one time that they got him on a blitz, he executed very well, he was sharp, he did exactly what we needed to do, even in the run game," Culley said.
"I just think he'll be a lot more comfortable now, simply because he has been out there and against a very good defensive football team."
He added: "We'll actually have the same playbook, obviously there's some things that he is a little different than Tyrod, but we actually have the same kind of plays.
"But we'll use the things that fit him more so than what we did with Tyrod. Some of the things we did with Tyrod we may not do with him in the run game, but as far as the pass game it will basically be the same thing."
Culley declined to offer up any timeframes on Taylor's likely return from injury, stating he was "not sure what the timetable is right now".
Taylor, who signed a one-year, $5.5million contract in Houston, was widely expected to be named the Texans' QB1 – a decision confirmed by head coach David Culley on Monday.
The Texans, for whom third-round rookie Davis Mills will serve as back-up, are set for a testing year.
Deshaun Watson has been the team's star QB over the past four seasons, last year leading the league in passing yards (4,823) and passing yards per attempt (8.87) – this despite being sacked 49 times, second only to Carson Wentz.
Watson was the one bright spot on a team that finished 4-12 in 2020, but he is not likely to feature this season despite remaining on the roster.
The 25-year-old in January asked for a trade, only for talk of a move to be overshadowed two months later by the emergence of sexual assault and misconduct allegations. Watson is the subject of investigations from the police and the NFL and faces 22 civil lawsuits.
Watson has not been restricted from taking part in team activities, yet a belated exit is anticipated after a period on the sidelines.
That leaves Taylor in the firing line on a team forecast to have the worst record in the league.
The 32-year-old was a regular for the Bills for three years between 2015 and 2017, but he has started only four games in three seasons since leaving Buffalo – three with the Cleveland Browns in 2018 and one last year with the Los Angeles Chargers.
Taylor completed only 16 of his 30 pass attempts in 2020, a small sample size providing a 53.3 completion percentage that paled next to Watson's 70.2.
The Texans start against the Jacksonville Jaguars and number one overall pick Trevor Lawrence on Sunday.
In his 11th season in the NFL, Taylor will play for his fifth team after stints with the Los Angeles Chargers, Cleveland Browns and Buffalo Bills since being drafted by the Baltimore Ravens.
According to a report from ESPN's Adam Schefter, the deal for the 32-year-old includes $8.5m in guaranteed money.
The Giants did not immediately confirm the deal, but Taylor changed his Twitter bio to identify himself as a "current New York Giant".
He also posted the tweet: "NYC!!!!!"
Taylor lost his starting role with the Chargers after an injection resulted in a punctured lung shortly before kick-off against the Chiefs in September 2020, with rookie first-round pick Justin Herbert getting the start and taking over as the franchise quarterback.
The Chargers went a disappointing 5-11 in 2019, which proved to be the last campaign of Philip Rivers' time with the franchise as the veteran QB departed after 16 seasons.
Though there was reported interest in Tom Brady, who chose the Tampa Bay Buccaneers as his next destination, the Chargers are yet to acquire another signal caller in free agency, leaving Taylor at the top of their depth chart.
Los Angeles could still select a quarterback with the sixth overall pick in the 2020 NFL Draft next month, though Taylor is confident he can turn their fortunes around if he is under center in Week 1.
"We have a lot of talent on our team," he told the Orange County Register.
"If I am the guy that would be calling the shots, I know for sure that we'll go out and turn a lot of heads."
Taylor was the Buffalo Bills' starting quarterback for three seasons and then began the 2018 campaign as the Cleveland Browns' starter, but he has still yet to shake the impression held by many that he is just a solid backup.
Entering his 10th year in the league, Taylor says that gives him extra fuel.
"It's motivating just for the highs and lows of my career," he explained.
"To be drafted in the sixth round, walking into my 10th year, there's definitely a lot of motivating factors in there being from my time when I was in Buffalo and when I played in Cleveland."
Taylor has spent the early stages of the offseason working with quarterback coach Jeff Christensen, who also happens to be working with free agent Cam Newton.
The 2015 NFL MVP has been linked to the Chargers following his release from the Carolina Panthers and those rumours only grew when Taylor was pictured practicing with Newton.
"It's just two guys working on their craft trying to get better," claimed Taylor, who has also worked out with Houston Texans QB Deshaun Watson recently.
"I wasn't implementing or trying to say anything with the photos. We were just out there working and the photos got sent. So no regrets, I posted it.
"We're really good friends and we're going to continue to remain friends, and we're going to continue to push each other and try to find ways to get better."
