Bruce Boudreau, after a short courtship with the Wild, will become the fifth coach in franchise history.

Boudreau, who coached the Anaheim Ducks and Washington Capitals to eight division titles in nine years, agreed to terms Saturday night on a four-year contract believed to be worth a shade under $3 million annually.

The 61-year-old Boudreau, nicknamed “Gabby,” is known as an up-tempo, offensive-minded coach.

The Wild extended the contract offer before Boudreau even left Ottawa on Saturday after interviewing for the vacant Senators coaching job on Friday. He’s expected to be introduced at a news conference Tuesday in St. Paul.

Wild General Manager Chuck Fletcher said there was no rush to name a coach, but the moment Boudreau was fired April 29 by the Ducks, Fletcher got in front of the line.

Last season, Boudreau became the fastest coach in NHL history to reach the 400-win milestone (663 games). He’s the seventh head coach in NHL history to win 200-plus games with multiple teams. In 681 regular-season games over nine seasons, Boudreau is 409-192-80. That .659 points percentage is tops in NHL history by any coach with more than 208 games. Hall of Famer Scotty Bowman ranks second at .657, and in 1,460 games and without the benefit of the shootout.

Bruce Boudreau was the fastest NHL coach to win 400 games, but his teams have struggled in the postseason.

Fletcher was unavailable for comment Saturday night, but at his end-of-the-season press event, Fletcher said, “I think it’s important that we find a coach that can hold the players accountable and put a system in place and get them to execute the system and hold them accountable to it.”

Boudreau couldn’t be reached for comment.

Fletcher contacted Ducks GM Bob Murray for permission to talk with Boudreau immediately after he was fired. He then spoke to Boudreau multiple times last Saturday and flew to California to meet with Boudreau on Tuesday.

Boudreau interviewed with the Senators all day Friday, but the Wild stepped up its contract offer Friday night. Former coach Mike Yeo, who is up for the Ottawa job and has a year left on his contract, is believed to make a hair over $1 million this upcoming season. So this is nearly $2 million more annually than owner Craig Leipold has ever invested in a coach.

Fletcher had to be aggressive from the outset, especially knowing that Ottawa would be an appealing job for Boudreau. Boudreau is from Toronto; his mother lives in St. Catharines, Ontario; and his daughter and granddaughter live in Ottawa.

Boudreau, who had a year left on his contract with Anaheim, coached the Ducks to four consecutive Pacific Division titles and a 208-104-40 record after coaching the Capitals to four division titles. He won the President’s Trophy (league’s best record) in 2010 and won the Jack Adams Trophy as the league’s Coach of the Year in 2008.

His undoing has been the postseason. He has only coached past the second round once, is 41-39 all-time in the playoffs, including 1-7 in Game 7s. In Anaheim, Boudreau suffered four consecutive Game 7 losses after the Ducks held 3-2 series’ leads.

Murray said April 29 that the way the last four years ended — “all very similar” — triggered the change in Anaheim.

“Nobody should think this is pointing the gun at Bruce’s head. Let’s make that perfectly clear,” Murray said. “But you’ve got to start somewhere. Regular season success is OK. … I want playoff success.”

Late Saturday, Murray issued a statement saying, “We felt that Bruce would be back behind the bench quickly. Everyone in the organization is very pleased he’s getting another deserved opportunity.”

Boudreau once played 30 games for the World Hockey Association’s St. Paul-based Minnesota Fighting Saints, was one of the top-scoring American Hockey League players in history (12th with 799 points and 16th with 316 goals) and coached ECHL and AHL teams to two championships. He ranks ninth in AHL history with 340 wins.

John Torchetti, who replaced Yeo as coach in February, was interviewed Monday for the job. He went 15-11-1 as coach and guided the Wild into the postseason for a fourth consecutive year. His status as of now is unknown and he could not be reached for comment. It’s believed he has another year left on his contract with the Iowa Wild.

Fletcher has said the new coach will have “free rein” to select his own assistant coaching staff. The Wild’s current assistant coaches have contracts that end June 30, sources say.