The 10-man competition, which raises money for charity, will also feature former world number one Ernie Els of South Africa, Britain’s Rory McIlroy and Americans Steve Stricker, Zach Johnson, Jim Furyk, Kenny Perry and Sean O’Hair.
World number one Woods, the defending champion this week who will be seeking a fifth Memorial title, won last year’s Skins Game with a dramatic chip-in.
A 14-times major winner who trails only Nicklaus (18) in the all-time standings, Woods returns to the PGA Tour after three weeks on the sidelines due to a neck injury.
Nicklaus, who hosts this week’s event at Muirfield Village Golf Club, will tee off in the first ‘skins’ group on Wednesday with Masters champion Mickelson, O’Hair, Perry and Els.
Woods will play in the second group alongside McIlroy, Stricker, Johnson and 2002 Memorial champion Furyk.
The Memorial Skins Game is a nine-hole event that offers a purse of $100,000 with proceeds benefiting The First Tee national youth development programme.