The foursome will play nine holes each day on the Celebrity Course at the Indian Wells Golf Resort.
Ames has won back-to-back Skins Game titles, pocketing more than $1.2 million in the process. Mickelson, meanwhile, will play in his third Skins Game, but first since 2003. He's never won the event.
Mediate has never played in the Skins Game, but his profile has never been higher. He lost a 19-hole playoff to Woods at the U.S. Open.
Choi is also a Skins Game rookie. He's 19th on the PGA TOUR money list and has three top-10 finishes this year, including a win at the Sony Open in Hawaii.
This will be the 26th edition of the Skins Game, which was first contested in 1983.