Dilshan, whose trademark 'Dilscoop' shot has enthralled crowds around the world, was player of the tournament at last year's World Twenty20 in England where his 317 runs at 52.38 helped power Sri Lanka to the Lord's final against eventual champions Pakistan.
The 33-year-old will join fellow overseas signings Yasir Arafat and Dwayne Smith, who helped Sussex win last season's Twenty20 Cup en route to the Champions League in India.
Sussex's professional cricket manager Mark Robinson said: "The recruitment of overseas players is becoming more complex as the international fixture list grows, including the possibility of staging major matches at neutral venues such as the UAE and USA.
"With Yasir Arafat likely to have Pakistan commitments and Dwayne Smith with the West Indies, the signing of one of the world's leading batsman gives us some exciting options.
"We want our main players to have genuine match-winning ability - and we believe we have that with Dilshan, Yasir and Dwayne.