Muralitharan's presence in Australia, where he has been reported for throwing before, had been in doubt since Australian Prime Minister John Howard branded him a "chucker".
The off-spinner met with Sri Lankan officials on Friday to discuss his decision and will confirm his withdrawal on Tuesday, the official said.
Although a contracted player, the board had given him the freedom to withdraw from the tour. His team mates had also said they would back any decision he made.
The 32-year-old Muralitharan, who has taken 527 wickets in 90 Tests, was reported to the International Cricket Council (ICC) by match referee Chris Broad during Sri Lanka's series against Australia in March for having a suspect action while bowling his "doosra" delivery.
The doosra is a delivery that spins in the opposite direction to his stock off break.
Biomechanical tests at the University of Western Australia showed Muralitharan's arm flexed by 10.2 degrees, double the five-degree level of bending allowed by the ICC and he was told to stop bowling it.
He played in Sri Lanka's comfortable Test series victory in Zimbabwe last month, taking 14 wickets to pass the record of 519 Test wickets held by Courtney Walsh of West Indies.
Muralitharan, who was called for throwing by Australian umpires during tours in 1995-6 and 1998-99, said earlier this month he had been upset by the latest controversy.
"The period since Chris Broad's report has been a most traumatic time for me," said Muralitharan. "I have been defamed, pilloried and severely criticized by the world's cricket media.
"Even the prime minister of Australia, John Howard, has called me a chucker."
"My action is unorthodox," he said. "It is, however, wrong for people to label me as a 'chucker' based solely on what they see with the naked eye.
"What such people perceive as a 'throw' is an 'optical illusion', a fact proven by the tests carried out on my bowling action over the years."
Sri Lanka begin their tour with a warm-up game against a Northern Territory Chief Minister's XI on June 24 before Tests in Darwin and Cairns.
