Oates also was named a 2012 Hockey Hall of Fame inductee on Tuesday.
"Obviously, a fantastic day. I don't know if that's happened before," Oates said of being picked for induction and hired as a coach on the same day. "It's just a special, special day for us."
Oates leaves the New Jersey Devils after two seasons as an assistant coach. He also was an assistant in Tampa Bay in 2009-10.
"He's been, certainly, a credit to us here," said Devils GM Lou Lamoriello about Oates. "He did an outstanding job for us. I wish him well.''
Oates replaces former teammate Dale Hunter, who stepped down after this past season. Hunter had replaced Bruce Boudreau in November. Hunter led the team to the second round of the playoffs as a midseason replacement before deciding he rather would be at home with his family, his farm and the junior club he owns in Canada.
Next up is Oates, 49, who played 19 seasons as a center in the NHL, including parts of six seasons with the Capitals from 1996-2002. His 290 assists rank 10th in team history, and he and Hunter were part of the 1997-98 team that made the only Stanley Cup finals appearance to date in franchise history.
"We are very pleased to name Adam Oates as the new head coach of the Washington Capitals," Capitals general manager George McPhee said in a statement. "Adam was a highly intelligent player in the NHL for 19 seasons. He has been an assistant coach in our conference for the past three seasons and is prepared to lead our club as head coach."
Oates will be formally introduced at a news conference on Wednesday.
His most formidable task will be to develop a playing style that best suits a Capitals roster brimming with talent that can also succeed in the playoffs. Led by Alex Ovechkin, Washington won four consecutive Southeast Division titles under Boudreau but couldn't advance beyond the second round of the postseason.
"I know a lot about him as a player," the Capitals' Troy Brouwer said in Chicago, where he's attending union meetings. "Obviously, being inducted into the Hall of Fame helps his credibility and his stature, but guys already know that he was able to do a lot of good things in his career. He was able to be a good offensive impact player on any team that he played for, and I think he's probably going to bring some of that mentality to our team."
Brouwer actually was hoping the job would go to Mike Haviland, an assistant in Chicago when he played there. Haviland recently was fired by the Blackhawks.
"He's had a lot of influence in my hockey career," Brouwer said. "I guess they went with Oates, and it was obviously a decision that they felt was best for the team. Any decision that they're going to make I think is going to be the one that they feel is going to propel the team into a good category."
Lamoriello said Oates had a great relationship with Ilya Kovalchuk and other players.
"There's no question. He's very communicative, very intelligent, he explains things very well," he said. "He has the resume behind him as a player and having the success he had -- all the credentials are there for having the kind of respect players have for him.''
Lamoriello said the future of Devils assistant coach Larry Robinson also is in doubt.
"Larry is just wondering exactly where he's at and what he wants to do. He's been there for a long time. I can't say for sure what he's going to do.''
Information from The Associated Press was used in this report.