By Agence France-Presse
The moderate was deposed in a Liberal party coup last week driven by a hardline conservative faction.
After being knifed, he indicated would leave parliament rather than go to the backbench and told a party gathering on Monday evening he will officially resign on Friday, broadcaster ABC and Fairfax Media reported.
His departure will trigger a by-election for his Sydney seat, potentially on October 6, leaving new Prime Minister Scott Morrison in a precarious position with no parliamentary majority for two weeks.
Turnbull's seat in the wealthy Sydney enclave of Wentworth is traditionally a Liberal safe haven, although a backlash against the government's political infighting could make this less certain.
"As you know, my prime ministership has come to an end. The circumstances have appalled most Australians but again, I won't labour the point," he told the Monday meeting, Fairfax reported.
"I have a strong view which I've made very clear publicly so it comes as no surprise, that former prime ministers are best out of parliament not in it, and I think recent events best underline the value of that observation.
"And so, accordingly, on Friday, I will resign from the House of Representatives."
Christine Forster -- the sister of arch-conservative Tony Abbott, who helped orchestrate Turnbull's demise -- has already put her hand up to replace Turnbull in the plum seat.
Forster, who is gay and was a high-profile proponent of same-sex marriage in a successful campaign last year, is a well-known Liberal councillor in Sydney.
Others reportedly in the running include businessman and former ambassador to Israel Dave Sharma, while the Greens and Labor will almost certainly field candidates.