The official announcement will be made at the ASEAN summit in Cambodia on Friday, the newspaper said.
"[ASEAN leaders agreed] in-principle to admit Timor Leste to be the 11th member of ASEAN," the leaked text of the announcement read, as quoted in the report.
The country will be granted observer status until it formalizes a "roadmap" to full membership in 2023, the leak said.
In July, East Timorese President Jose Ramos-Horta said that it was easier to enter heaven than ASEAN.
East Timor has been seeking membership in ASEAN ever since gaining independence from Indonesia in 1999. It formally applied for membership in 2011.