Spain's Rahm will launch his run at a first major crown in the group after Johnson, playing alongside England's Paul Casey and US star Phil Mickelson, the 50-year-old left-hander who has a heartbreak history at Winged Foot.
Mickelson came to the 2006 US Open at Winged Foot off wins at the 2005 PGA and 2006 Masters and led by a stroke at the final tee on Sunday needing only a par for victory.
Instead, Mickelson's driver shot off the tee went left into a corporate hospitality tent, landed in trampled down grass and allowed him a chance to shoot for the green.
Mickelson took his chance but hit a tree and he then plugged his ball into a greenside bunker on his third shot. Mickelson chipped over the green, missed his chip-in bogey attempt and handed the title to Australian Geoff Ogilvy.
Mickelson, who needs only win the US Open to complete a career Grand Slam, has settled for second place at the US Open a record six times.
Starting in the group ahead of Johnson is the defending champion, Gary Woodland, who plays alongside fellow American Andy Ogletree, the 2019 US Amateur champion, and reigning British Open champion Shane Lowry of Ireland.
This year's British Open was called off due to the coronavirus outbreak while the Masters was postponed from April to November.