Dilshan will be holding a press conference tomorrow to make a formal announcement.
"I have taken this decision to allow Sri Lanka Cricket to groom another youngster in my place," Dilshan said.
"I was to announce my retirement after the Zimbabwe Test series but unfortunately the tour was postponed," he added.
Sri Lanka were initially scheduled to tour Zimbabwe in October, which included two Tests.
The aggressive opener, however, expressed his desire to continue to play in the shorter formats of the game.
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In a Test career spanning 14 years, the 36-year-old opener played 87 matches, scoring 5492 runs at an average of 40.98. He made his debut against Zimbabwe in 1999 at Bulawayo. His 16 Test centuries included a career-best 193 against England at Lord's in 2011 when he was the captain of the side.
The Kalutara-born player has also taken 39 wickets with a personal best figures of four for 10 against Bangladesh in Chittagong in 2009.