Price went for Australian Steven Bowditch and Korean Bae Sang-moon to round out his 12-man International lineup for the Oct.
8-11 matches at Jack Nicklaus Golf Club in suburban Seoul.
Haas will be making his third appearance in the biennial team competition while Mickelson will extend his record run to 11, having played in every edition since the Presidents Cup was launched in 1994.
The selection of Haas was always likely as the 33-year-old won his sixth PGA Tour title at the Humana Challenge in January and finished 11th in the Cup standings, just one spot shy of automatic qualification.
Five-times major champion Mickelson, however, languished in 30th spot, having not triumphed on the PGA Tour since the 2013 British Open, though his form has steadily improved in recent months.
“Phil has made the past 20 Ryder Cups and Presidents Cup teams without needing a pick so, if anyone deserves a pick, it’s Phil Mickelson,” Jay Haas said of the 45-year-old.
“He was without question the leader of our team in the team room and on the golf course. The guys on the team were adamant that Phil was the guy.”
Mickelson record in the Presidents Cup is 20 wins, 16 losses and 11 halves.
Haas said that his son had always been likely to get picked as the 11th player in the standings and that, like Mickelson, he had been hugely supported by the players and assistant captains.
“Bill deserves this as much as anybody,” said Haas senior. “He’s had a wonderful year.”
Bowditch ended up 11th in the International standings and was a likely choice by Price after clinching his second career victory on the PGA Tour at the AT&T Byron Nelson in May and producing consistent form this season.
Bae got the nod over Australian Matt Jones, despite finishing 19th in the standings, and will give Price his second Korea-born player at this year’s Presidents Cup, alongside New Zealander Danny Lee.
“It was a difficult decision … I chose him because he has played pretty well the last couple of weeks but also because he has won on the golf course in Songdo, the Jack Nicklaus Golf Club, the last two years on the Korean Tour,” said Price.
“It was also very important for us to have someone on the team that the Korean fans and the media could pull for.”
The U.S. have dominated the Presidents Cup, winning eight times in 10 editions, including a victory by 18-1/2 points to 15-1/2 in the most recent encounter at Muirfield Village in Dublin, Ohio two years ago.
The only success for the Internationals came in 1998 when the event was held at Royal Melbourne in Australia. In 2003, the two teams battled to a 17-17 draw in South Africa.
(Reporting by Mark Lamport-Stokes in Las Vegas; Editing by Andrew Both)