Djokovic, who had a knee operation after pulling out before his French Open quarter-final, is chasing a record-equalling eighth men's Wimbledon title and opens against Czech qualifier Vit Kopriva.
Britain's Murray, a two-time champion, takes on another Czech, Tomas Machac, just over a week after having surgery to remove a cyst from his spine, in his farewell appearance at the tournament.
Also in action on the second day of the Championships is women's world number one and five-time Grand Slam champion Iga Swiatek, eager to progress beyond the quarter-finals for the first time.
AFP Sport looks at three matches to watch on Tuesday:
Novak Djokovic v Vit Kopriva
World number two Novak Djokovic has declared himself "pain-free" after initial fears he would miss Wimbledon following surgery to repair a torn meniscus.
The Serbian has not played since he was forced to withdraw from the French Open before his last-eight tie against Casper Ruud.
Now 37, he knows time is not on his side as he bids to equal Roger Federer's Wimbledon record and become the first player -- man or woman -- to win 25 Grand Slam singles titles.
Djokovic, who practised with a knee support on Sunday, said he had an "incredible desire" to play".
He arrives in London without a title to his name this season, losing his Australian Open crown and the number one ranking to 22-year-old Jannik Sinner.
The Serbian, who has reached the past five finals at Wimbledon, faces Vit Kopriva, ranked 123rd, for the first time in his career.
Andy Murray v Tomas Machac
It has been a case of "will he or won't he?" in the build-up to Wimbledon for home hero Andy Murray after his operation just over a week before the start of the tournament.
The 37-year-old is hoping to finish his career at the upcoming Paris Olympics but desperately wants to make a final appearance in London.
The injury-ravaged Scot has slipped to 113th in the world rankings but it now appears he will get his dream of a send-off at Wimbledon, where he is also listed to play doubles alongside brother Jamie.
The former world number one is due to face 39th-ranked Tomas Machac on Centre Court on Tuesday, with emotions running high.
The Czech player leads 2-0 in head-to-heads, with both wins coming this year.
"I'm hoping maybe for a bit of closure," said Murray, who won the Wimbledon title in 2013 and 2016.
"I just want the opportunity to play one more time out there, hopefully on Centre Court, and feel that buzz."
Iga Swiatek v Sofia Kenin
World number one Iga Swiatek arrives at the All England Club on the back of a 19-match winning streak but with lingering questions over whether she can transfer her clay-court form to the grass.
Swiatek, who has won five trophies already this year, has not played a warm-up tournament on grass, opting to withdraw from the Berlin event in order to rest.
Last year's quarter-final appearance was her best showing so far at Wimbledon but the Pole, 23, is justifiably tipped to go far at this year's Wimbledon, where she clinched the junior title in 2018.
First up is Sofia Kenin, whom Swiatek defeated in the first round of the Australian Open this year.
The 49th-ranked US player has struggled this season but she has experience of the sharp end of Grand Slams, triumphing at the 2020 Australian Open before losing to Swiatek in the final of the French Open months later.
