Swinney's salary and possible incentives in the deal won't be released until the contract is approved by the university's Board of Trustees Compensation Committee.
Athletic director Terry Don Phillips said Swinney was one of college football's bright young coaches and he was proud to lock him up long-term.
"He took over a very difficult situation for the last six games and showed me what type of coach and leader he is," Phillips said in a statement. "I was impressed by the way the team responded to his leadership."
Clemson players assembled at the team's football offices at the McFadden Building for Phillips to introduce their new, old coach. Phillips and Swinney were expected to meet the media later Monday.
Swinney took over as interim coach Oct. 13 when Bowden resigned.
The Tigers won four of their final five games under Swinney to become bowl eligible. The clincher came Saturday when Clemson defeated rival South Carolina 31-14.
Phillips had traveled the country interviewing candidates the past month, including soon-to-be Tennessee coach Lane Kiffin and coordinators like Bud Foster of Virginia Tech and Brent Venables of Oklahoma. Turns out, Clemson's best choice was a building away from Phillips' office.
The two met Sunday for a formal interview.
Phillips was all smiles Saturday afternoon after Clemson's victory, watching Swinney get carried off the field by his players. Phillips declined to discuss Swinney's future then, saying he wanted Saturday to be about Clemson's coaches and players and what they had accomplished under difficult circumstances.
A big reason was Swinney.
William Christopher Swinney was born in Birmingham, Ala., and got his nickname because an older brother had trouble pronouncing "that boy." Swinney walked on to the Crimson Tide football team and eventually earned a scholarship and a national championship ring with coach Gene Stallings' 1992 squad.
"I could tell there was something special about Dabo as far as being a coach," Stallings said last week when he visited Clemson's practice.
Swinney stuck with Stallings' staff and stayed at Alabama through 2000.
He was selling real estate in early 2003 when Bowden, once his Alabama position coach, called him about a Clemson opening. Swinney has been the Tigers' receivers coach and one of the team's top recruiters - he lured star runner C.J. Spiller out of Florida's backyard - until becoming head coach at Bowden's suggestion to Phillips in October.
Among Swinney's first moves was firing offensive coordinator Rob Spence, almost as big a lightning rod for fans' displeasure as Bowden, and taking over the play-calling.
Swinney started a "Tiger Walk" through the parking lot to the stadium before games so players could feel the support of Clemson's faithful.
He opened practice to students and, sometimes, canceled workouts to take the players to a children's hospital to lift patients' spirits.
Swinney, 39, was folksy and charming, comparing Clemson's problems to a poorly tuned car that just needed a little TLC.
Swinney's biggest move was rediscovering playmakers like quarterback Cullen Harper, receiver Aaron Kelly, and the "Thunder and Lightning" runners of James Davis and Spiller.
Harper was banged up and ineffective in September before getting benched by Bowden right before the change. Swinney put the ball back in the senior's hands, and he responded with seven of his 11 TD passes the last six games.
Kelly, a senior, was much more effective the second half of the year. Davis and Spiller have combined for 10 scores the last six games.
The Tigers needed a finishing flourish to keep playing past November. The win over South Carolina, Clemson's third in a row, got that done. Swinney and the team await their bowl destination, something few figured possible when the interim coach nervously met the media his first night on the job.
The pick is sure to be popular with the players, who had hoped he'd return.
"I feel like he's turned this program around in some great ways and he has a bright future here," safety Michael Hamlin said Saturday.