The island country has been without a full-time head coach since South African Mickey Arthur stepped down late last year.
"I am very excited to be on board with Sri Lanka and I cannot wait to get over to Colombo and get started," Silverwood said in an SLC statement.
"They have a talented and passionate group of players and I am really looking forward to meeting up with the players and coaching staff very soon."
Silverwood stepped down from his England position in February after the team lost the five-test Ashes series in Australia 4-0.
His first assignment with the Sri Lankan team will be a two-Test series in Bangladesh next month.