Sutton met with PGA of America executives last week during the Disney World Golf Classic, according to a PGA Tour source who spoke only on condition of anonymity. He decided to accept the job after talking it over with his family, the source said.
The PGA of America said the captain will be announced Thursday.
The 2004 matches will be played at Oakland Hills Country Club outside Detroit.
Sutton will be in charge of bringing the Ryder Cup back to the United States after the Americans lost to Europe at The Belfry by the largest margin in 17 years. Europe has taken the Ryder Cup home after six of the past nine meetings.
U.S. captain Curtis Strange was criticized for putting his best two players -- Phil Mickelson and Tiger Woods -- at the bottom of the lineup, although Mickelson wound up losing a critical match to Phillip Price, ranked 119th.
Sutton was asked last week at Disney about the criticism that losing Ryder Cup captains always receive, saying that would never keep him from accepting the job.
'The neat part about that is you're in a big enough position that everybody not making that decision can sit around and criticize you,' Sutton said. 'If you're afraid to be second-guessed, you better not make any decisions.'
Paul McGinley clinched the Ryder Cup for Europe by making a 12-foot birdie on the 17th hole to square his match with Jim Furyk, then tying the final hole for a half-point by making an 8-foot par putt.
'We shouldn't lose these things the way we're losing them,' Sutton said last week. 'There's way too much talent over here.'
Asked about his prospects of being a Ryder Cup captain, Sutton said at Disney that he would be honored if asked.
'Making Ryder Cup teams, whether as a player or a captain, is what you strive to do when you're young or old,' he said.
Reached on his cell phone Tuesday, Sutton declined to confirm his selection.
He will be 46 at the next Ryder Cup, although he still plans to play a full schedule on the PGA Tour next year. One reason he was thought to be hesitant about the offer was the appearance that he was giving up on his tour career.
He has won 14 times in a career of amazing peaks and shocking lows.
Sutton was considered golf's next star when he beat Jack Nicklaus in the 1983 PGA Championship at Riviera. He won seven times in his first five years, but then went into a deep slump, winning just one tournament over the next 11 years.
His return to top play was just as stunning.
He won the 1998 Tour Championship, one of six tournaments he has won since turning 40. Another was The Players Championship in 2000, when he went toe-to-toe with Woods in the final round and beat him by one stroke.
Sutton played on four Ryder Cup teams, none more memorable than 1999, when he was the anchor of a U.S. team that rallied to beat Europe at Brookline. Sutton went 3-1-1.
He has had nagging back injuries and sleep apnea the last 18 months, but still rallied to win an alternate-shot match with Scott Verplank at The Belfry. Sutton was 1-1, losing to Bernhard Langer in singles.
Europe's captain is expected to be chosen by the end of the year. Langer and Ian Woosnam are among the candidates.