Atapattu, 43, was appointed for the tour of England and Scotland starting next month and the subsequent home series against South Africa in July, the board said in a statement.
Former Test spinner Ruwan Kalpage will join Atapattu as assistant coach for the same period, the statement added.
Atapattu replaces Englishman Paul Farbrace, who quit earlier this week after just four months on the job to take over as England's deputy coach under Peter Moores. Atapattu, a right-hand batsman, played 90 Tests, 268 one-dayers and two Twenty20 internationals in a career that spanned 17 years before he retired in 2007.
He scored 5,502 Test runs at an average of 39.
02 with 16 centuries. His 8,529 one-day runs included 11 hundreds.
Atapattu will be the latest addition in a succession of coaches for Sri Lanka since 2010, following Trevor Bayliss, Stuart Law, Rumesh Ratnayake, Geoff Marsh, Graham Ford and Farbrace.