Billups spent the 2020-21 NBA season as Los Angeles Clippers assistant coach and has given been the chance to take the top job at Portland.
The five-time All-Star replaces Terry Stotts, who departed after the team's elimination in the opening round of the NBA playoffs this month.
Billups, named Finals MVP when the Detroit Pistons were crowned champions in 2004, is relishing a new challenge with the Trail Blazers.
The 44-year-old said: "I'm very excited and humbled to be the next coach of the Trail Blazers.
"Portland is a special place and a unique franchise. As a player I always loved playing here because the passion and knowledge of the fans brought out the very best in me as a competitor.
"Now I'm looking forward to being on the other side of that energy and engaging with the Portland community on a whole other level.
"I want to thank Jody Allen, Bert Kolde and Neil Olshey for their trust and for giving me this incredible opportunity. And, most importantly, I want to say to the fans that I know what this team means to you, and I promise to pour every ounce into continuing to make you proud of what the Trail Blazers stand for."
Trail Blazers chair Allen said: "Chauncey is a proven and consistent winner with NBA championship experience as an All-Star NBA player.
"He has demonstrated throughout his career, first as a player, and currently as an assistant coach a unique ability to lead. We are very happy to welcome him to Portland."
Billups played 17 seasons in the NBA for Boston Celtics, Toronto Raptors, Denver Nuggets, Minnesota Timberwolves, Detroit, New York Knicks and the Los Angeles Clippers.
Washington looked set to extend their winning streak to seven games on Friday, only for Portland to stage a third-quarter fightback in a 124-116 victory over the Wizards.
Anfernee Simons scored 20 of his 33 points in the third quarter, making six of Portland's nine three-pointers in the third, as he went on to finish 9-of-12 beyond the arc.
"Our team is just so much better when our backs are against the wall," Billups said. "I've been on teams like that before, so I understand it, but it's a dangerous place to live."
A fine comeback saw the Trail Blazers fire nine field goals from long distance after going in at the second quarter 69-51 down.
Simons hit the first five of those shots before hitting another three-pointer to reduce the deficit to seven points after scores for Damian Lillard and Jerami Grant.
The Trail Blazers eventually snatched the lead at 102-101, but Portland could not have fought back without Simons.
"We ran plays for him. We started off the third quarter kind of running his play," Billups said. "He came off and got a couple of looks.
"Then I thought Dame and Josh and those guys, they all just did a really good job of continuing to keep the ball in his hands."
The 62-point margin of defeat was the joint-fifth largest in NBA history and marked a record victory for the Thunder in franchise history.
Shai Gilgeous-Alexander registered 31 points at Paycom Center and Jalen Williams 21, while Josh Giddey had a triple-double.
"It was almost like a perfect storm, to be honest with you," Billups told reporters after the game. "Nothing really worked for us.
"I mean, this was, sheesh – not much really good to say about this one for us.
"I thought that we generated some pretty good looks in the first half. The fact that we couldn't make pretty much anything deflated us."
Only once before have the Trail Blazers been on the end of a worse defeat – a 65-point loss to Indiana Pacers in 1998.
The victory for Oklahoma City was their third in a row, having also defeated the Miami Heat and the Washington Wizards this week.
Coach Mark Daigneault was particularly pleased with how his side adapted after returning home in the early hours of the same day.
"I thought we cleared a couple hurdles tonight," Daigneault said.
"The first one was the start of the game, how ready we were to play and the energy we were able to generate with a tough schedule.
"It's mind over matter. And then the other hurdle was playing with a lead. I thought we played pretty well with a lead, both ends of the floor."
Oklahoma City's previous record margin of victory was 45 points, which they registered twice in the 2012-13 season.
The 26-11 Thunder are level with the Minnesota Timberwolves for the best record in the Western Conference. Portland are 10-27 and are in 14th.
