The confirmation was conveyed to Sri Lanka Cricket in an email sent to it.
Perera replaces Muralitharan after medical reports were received indicating that the champion off-spinner had sustained an injury to his right distal bicep and would not be fit in time to take part in the event, which will be held from Sept 11 to 24.
Sri Lanka's first match of the inaugural ICC World Twenty20 in South Africa will take place against Kenya at Johannesburg on Friday Sept 14.
The 25-year-old Perera, an uncapped off-spinner, is the second replacement player to be called up for the tournament so far after Ben Hilfenhaus was replaced by Shaun Tait in the Australian squad.
The process required for approving any player involves that player's home board making an application in writing to the tournament's Technical committee for permission.
In this case the application was supported by medical reports confirming Muralitharan's injury and certifying that the player was not fit for the event.
The Technical committee of the ICC World Twenty20 consists of David Richardson (International Cricket Council), Campbell Jamieson (IDI, the ICC's commercial arm), Steve Elworthy (tournament director), Brian Basson (Cricket South Africa), Ravi Shastri (Independent) and Ian Bishop (Independent).
Fixture: Twenty20 World Championship