The biennial competition, which pits a 12-man team from the United States against a line-up of international players from outside Europe, will be played in South Korea from Oct. 8-11 at the Jack Nicklaus Golf Club in Songdo, marking the first Presidents Cup to be staged in Asia.
Price, who played on five Presidents Cup teams, was captain at the 2013 matches at Muirfield Village in Dublin, Ohio, won by the U.S. team 18-1/2 to 15-1/2.
"I'm delighted to be asked to do this again," Price said at a news conference presenting the captains in Ridgedale, Montana, site of this week's Champions Tour event. "Last year was a learning experience for me."
Price named Korean PGA Tour member K.J. Choi as his vice captain and said it was appropriate the event, which alternates between U.S. and international venues, has come to South Korea, which has become a "powerhouse in golf."
Choi said it would be a great pleasure to work with Price.
"People in Korea are thrilled and excited about this event," said Choi. "Seeing the Presidents Cup played in Korea will be the most incredible experience for my country.
"I hope that we will win this time."
Haas played on three Presidents Cup teams and served as an assistant to captain Fred Couples in the last three events, which were won by the U.S. side. His son, Bill, played on the previous two U.S. teams.
Haas returned the favor by naming Couples as one of his assistants.
"We've been buddies for a long time and I look forward to our going to South Korea and putting up a good fight," Haas said.
The U.S. team has won the Presidents Cup eight times while the International side has won once with one competition ending in a draw.
(Reporting by Larry Fine in New York; Editing by Frank Pingue)