The trio will tee-off in the opening round at 0933 local time at St Andrews, organisers said on Monday.
Spieth is bidding to emulate compatriot Ben Hogan who was the last man to win the U.S. Masters, the U.S. Open and the British Open in the same season.
The big-hitting Johnson missed an eagle putt for victory at last month's U.S. Open and went on to suffer the heartbreak of taking three putts at the final hole.
Spieth, 21, goes into golf's oldest major in red-hot form having also beaten compatriot Tom Gillis at the second hole of a playoff to land the John Deere Classic title in Silvis, Illinois on Sunday.
Former world number one Tiger Woods, who won the Open at St Andrews in 2000 and 2005, starts his campaign for a 15th major title at 0955 alongside 2010 winner Louis Oosthuizen of South Africa and Australian Jason Day.
Phil Mickelson, the 2013 Open champion, tees off with Sweden's Henrik Stenson and fellow American Matt Kuchar at 1434.
American Rickie Fowler, winner of Sunday's Scottish Open at nearby Gullane, will partner six-times major champion Nick Faldo and world number eight Justin Rose at 1445.
Five-times Open winner Tom Watson, 65, who is making his swansong appearance in the tournament, accompanies fellow American Brandt Snedeker and Ernie Els of South Africa at 0833.
The honour of hitting the first shot of the championship belongs to Australian Rod Pampling who goes out at 0632 alongside Dane Thomas Bjorn and Britain's Greg Owen.
(Editing by Ed Osmond)
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