Dilshan will lead the side in all three formats of the game -- Tests, one-day internationals and Twenty20s -- on the tour, Sri Lanka Cricket said in a statement.
The 34-year-old, renowned for an over-the-head scoop shot dubbed the "Dilscoop", replaces Kumar Sangakkara, who stepped down after Sri Lanka lost the World Cup final to India earlier this month.
Fitness worries meant the five-member national selection panel headed by Duleep Mendis, a former Sri Lanka skipper, did not name a vice-captain.
"The prospective candidates are nursing injuries and their availability for the forthcoming tour is still in question," the statement said.
All-rounder Angelo Mathews, 23, has been tipped for the role, but he is nursing a side strain suffered during the World Cup semi-final.
Dilshan, a right-handed batsman currently playing in the Indian Premier League, is expected to travel to Colombo this week to meet the selectors and pick the squad for England.
The tour runs from May