Mickelson, DeChambeau and Fleetwood among early British Open starters
Six-times major champion Mickelson tees off at 7:30 local time (8:30 CET), two groups ahead of DeChambeau, the long-hitting 2020 US Open winner who will play with American John Daly (56), the Open champion at St Andrews in 1995.
Defending champion Collin Morikawa goes out with world number two Rory McIlroy (33) and in-form American Xander Schauffele.
"I am the defending champ, but we're at a different golf course. We're at a course I've never been to," Morikawa said.
"Even though my week is filled with a couple of extra media obligations doesn't mean by Thursday morning I'll not be ready. Through two days (here) so far I've done a pretty good job of figuring out what I'm going to do."
McIlroy won the British Open and the USPGA Championship in 2014 to move on to fourth major titles, but he has not added to that haul since.
"I've only played one Open here before," McIlroy told reporters on Tuesday. "I'm playing well. I'm in good form. My confidence in my game is as high as it's been in quite a while.
"I can't go in here thinking that this might be my time. I just have to go out and play a really good tournament. I've got to string four good rounds together."
Tiger Woods, twice Open champion at St Andrews, begins his bid for a 16th major title alongside Briton Matthew Fitzpatrick who won this year's US Open.
World number one Scottie Scheffler will play with Chile's Joaquin Niemann and Briton Tyrrell Hatton while 2017 Open champion Jordan Spieth is also among the later starters in a group including world number three Jon Rahm of Spain.
Italian Francesco Molinari, the 2018 Open champion, is among the early starters alongside Britons Justin Rose and Tommy Fleetwood.
Scotland's Paul Lawrie, the 1999 Open champion, will have the honour of hitting the first ball of the tournament at 6:35 local time.
"It's always nice to hit the opening shot," Lawrie said. "Looking forward to it. It's a huge week, a big milestone. The more you think about it, it's a nice thing to be asked to do at the 150th Open."