Cink is the fifth and final vice captain, joining Steve Stricker, Davis Love III, Jim Furyk and Fred Couples when the Americans face Team Europe Sept. 29-Oct. 1 at Marco Simone Golf & Country Club in Rome.
It will be Cink's first time serving in this capacity. He played on five straight U.S. Ryder Cup teams from 2002 to '10.
"Competing in the Ryder Cup has been one of the highlights of my entire career and I'm ready to do whatever it takes to help Zach and the U.S. Team retain the Ryder Cup," Cink said in a news release. "I'm honored that Zach would entrust me to play a role in helping make that a reality in Italy."
Cink turned 50 earlier this year and is playing on both the PGA Tour and the PGA Tour Champions. He has won eight times in his career on the PGA Tour, including The Open Championship in 2009.
Johnson is serving as team captain for the first time after previous appearances as an assistant captain at the Ryder Cup and Presidents Cup.
"Stewart is someone I can trust will give me honest and constructive feedback as we head into the final stages of preparing for the Ryder Cup," Johnson said in a statement. "And as everyone saw at The Open Championship this year, he's still competing at a high level on the golf course. He will play a critical role in our success as we head to Italy."