Furyk, 46, played on nine straight Ryder Cup teams from 1997-2014. He compiled a 10-20-4 individual record across that span before serving last year as an assistant captain for Davis Love III as the Americans won the biennial matches for the first time since 2008.
"This is such an honor. I'm actually a little overwhelmed, didn't think it would be that way," Furyk said. "In my opinion, the Ryder Cup embodies everything that is special about golf."
The committee that chose Furyk included PGA of America president Paul Levy, CEO Pete Bevacqua and vice president Suzy Whaley as well as Tiger Woods, Phil Mickelson and Love, who captained the team in both 2012 and 2016.
Furyk has won 17 times on the PGA Tour, including the 2003 U.S. Open. While he missed much of last season because of a wrist injury, he returned to finish runner-up at the U.S. Open at Oakmont before firing a Tour-record 58 during the final round of the Travelers Championship in August.
In his first act as captain, Furyk announced that Love will serve as one of his assistants next year in France.
"Davis is going to be a tough act to follow. He put a system in place, got the players behind it," Furyk said. "His experience, two captaincies and a vice captaincy, will be priceless for me, so I'm happy to have him by my side."
Denmark's Thomas Bjorn was named European captain last month. Furyk will now take on the task of becoming the first American captain to hoist the trophy in Europe since Tom Watson won the 1993 Ryder Cup at The Belfry in England.
"Their fans provide an atmosphere that is electric," Furyk said. "The first tee at Gleneagles (in 2014) was absolutely amazing for both sides, but obviously their side is loud and they're cheering for their team. It's just like with any other sport. So we'll have our work cut out for us, it's been a long time. But I'm really looking forward to the challenge."