"He will be the new interim coach," a spokesman for Sri Lanka Cricket, the governing body of the sport in the island, said.
Law has been assisting Sri Lanka's outgoing Australian coach Trevor Bayliss since November 2009.
Sri Lanka tour England in the second week of May for three Tests and five one-day games.
Bayliss, who managed the team for four years, announced his decision to quit ahead of the World Cup 2011, which Sri Lanka lost by six wickets to India in the final. He is due to coach New South Wales.
Law's interim appointment comes amid a major shake-up in Sri Lanka cricket following their World Cup defeat.
Veteran batsman Mahela Jayawardene quit as vice-captain and a three-member selection committee resigned Wednesday, a day after skipper Kumar Sangakkara gave up his position.
Sangakkara stood down on Tuesday to allow selectors to groom new leaders for the next cricket World Cup in 2015
