CMC Sport said that Sarwan had been given the job at a meeting of the West Indies Cricket Board (WICB) yesterday.
The WICB were not immediately reachable for confirmation.
The 26-year-old right-handed batsmen from Guyana had been widely tipped to take the job for the upcoming tour of England.
The first test is on May 17.
Sarwan, who was Lara's vice-captain, has played in 65 test matches and 124 one-day internationals.