The pair will meet in the morning fourballs, along with Charles Howell III and South Africa's Tim Clark who will play with Woods and Els respectively in the United States v Internationals team match.
Woods holds a 3-1 winning record over world number three Els at the Presidents Cup, although they have never met in singles in a rivalry that goes back to 1998.
Woods and Howell started the 2003 matches successfully by winning their foursomes by 4 and 3 over Australia's Stuart Appleby and South Korea's K.J. Choi on Thursday.
But the U.S. trail 3-1/2 to 2-1/2 after the first day's play.
Els partnered Australia's Adam Scott to a one-up victory over Justin Leonard and Jim Furyk.
"After all the support Tiger had today, we'll see if he has it when he meets Els," U.S. team captain Jack Nicklaus said, referring to the strong support the American received from the South African galleries.
International captain Gary Player changed every one of the his pairings around after the successful foursomes for Friday's fourballs, while the U.S. team has retained three of the same pairings.
Phil Mickelson and David Toms will be first out against Australia's Robert Allenby and Canada's Mike Weir, followed by Kenny Perry and Davis Love III against South African Retief Goosen and Choi.
The third match sees Furyk and Jay Haas take on the Australian duo of Stuart Appleby and Scott.
Chris DiMarco and Leonard are paired against the U.S. Tour's leading money winner Vijay Singh and Zimbabwean Nick Price before the Woods/Els duel. Play starts at 0515 GMT.
