Leonard, who won the 1997 Open at Troon, was given the honours of launching the 152nd Open Championship alongside fellow American and another former winner Todd Hamilton.
Attention will turn to the world's top two players later as they aim to make a mark on the final major of the year.
McIlroy is aiming to get over his heartbreak at the US Open last month, where he blew a late lead due to two short missed putts as Bryson DeChambeau claimed his second major by one shot.
That extended the world number two's decade-long wait to add to his four major titles.
McIlroy has finished in the top 10 in five of the last seven British Opens, part of his 21 top-10 finishes since last winning a major.
"I'd much rather have these close calls. It means that I'm getting closer," said the Northern Irishman, who also missed out narrowly at the 2022 British Open and 2023 US Open.
McIlroy begins his quest at 09.09GMT alongside Max Homa and Tyrrell Hatton.
World number one Scheffler has won six times in just 14 starts this year and is aiming to make an impact across the Atlantic for the first time as he tees off at 1410GMT.
The American's best previous showing at the British Open was a tie for eighth in 2021.
Scheffler won his second Masters in April but has failed to add to his two majors since at the USPGA Championship and the US Open.
In-form DeChambeau
The form player at the majors has been DeChambeau, despite his defection to the breakaway LIV Tour.
The American finished sixth at the Masters and runner-up in the USPGA Championship behind a record-breaking 21 under par set by Xander Schauffele before claiming his second US Open.
DeChambeau has previously struggled with the windy conditions of links golf and recognised the need to alter his game on the west coast of Scotland this week.
"Controlling that golf ball underneath the wind is going to be super key this week," said DeChambeau, whose previous best finish at the British Open was a tie for eighth two years ago.
"I hit the golf ball really high, so it's always been a bit of an issue. I've got to keep the ball under the wind a bit more, keep a lower flight."
Tiger Woods makes his return to the event after missing last year's Open.
The three-time winner hit back at claims from former European Ryder Cup captain Colin Montgomerie that he should retire after playing sparingly and struggling since a serious car accident in 2021.
Indeed, Woods believes the conditions on a links course give him a better chance to compete than the longer hitting needed in the US.
"The older you get the less you can carry the golf ball but over here, you can run the golf ball 100 yards if you get the right wind and the right trajectory," said the 15-time major champion.
"I think that's one of the reasons why you see older champions up there on the board because they're not forced to have to carry the ball 320 yards any more."
Home favourite Bob MacIntyre tees off in one of the featured groups alongside 2023 Ryder Cup teammates Jon Rahm and Tommy Fleetwood at 0836 GMT.
MacIntyre stormed to Scottish Open success last weekend to back up his first PGA Tour win at the Canadian Open in June.
Defending champion Brian Harman begins his defence alongside Viktor Hovland and Sahith Theegala at 08.58GMT.
