A three-time winner of the event, Woods, 43, has never played in the format that has 16 groups of four players, with each group's leading point-earner after three matches advancing to the 16-player knockout stage on the weekend.
Players were divided by their world ranking after the Players Championship, which meant Woods was 13th. A random drawing then selected players from groups ranked 17th to 32nd, 33rd to 48th and 49th to 64th.
Cantlay, 27, ranked 18th, won the Shriners Hospitals for Children Open in 2017 for his lone PGA Tour victory.
Snedeker, 38, ranked 44th, is a nine-time PGA Tour winner whose last victory came at the Wyndham Championship in 2018.
Wise, 22, ranked 61st, is in his second year on the PGA Tour, having won last year's AT&T Byron Nelson Championship. Woods will face Wise, with whom he has never played, on Wednesday at 2 p.m. ET.
Woods last played in the WGC-Match Play in 2013, when the old knockout format was in use. That year, Woods lost his first-round match to Charles Howell III. Woods was eligible for the event in 2014 and 2015 but skipped the tournament; the last three years, injury curtailed his play, and he was not eligible last year, as he was ranked 105th in the world at the time of the tournament.
The format calls for 18-hole matches, with the best record from each group advancing. Matches can end in ties. If two or more players are tied after the three matches are completed, they go to a sudden-death playoff to determine who advances to the weekend.
There will then be eight matches on Saturday morning, followed by four on Saturday afternoon.
The top four then advance to the semifinals on Sunday, with the winners squaring off the title.