A trailer featuring the number 13 in different locations was aired during the tennis on BBC One on Friday.
It finished with the caption: "Meet the 13th Doctor after the Wimbledon men's final, Sunday 16th July."
The actor will succeed Peter Capaldi who took the role in 2013 and will leave in the 2017 Christmas special.
Capaldi made the announcement during an interview with BBC Radio 2 presenter Jo Whiley in January.
The Glasgow-born star said: "I feel it's time to move on. I feel sad, I love Doctor Who, it is a fantastic programme to work on."
The locations in the trailer included 10 Downing Street, Beachy Head cliffs and the Statue of Liberty.
The popular sci-fi series features a Time Lord, known only as The Doctor, who travels through time and space in the Tardis, which resembles a 1960s police telephone box.
The main character has the ability to regenerate, a quirk that has allowed a number of actors to have played the role over the years.
Capaldi, who replaced Matt Smith as The Doctor, was previously best known for his role as foul-mouthed spin-doctor Malcolm Tucker in the BBC series The Thick of It.
The identity of Doctor Who's 13th Time Lord will be revealed following the Wimbledon men's singles tennis final on Sunday, the BBC has announced.