The 29-year-old has moved to the Scottish capital from Sale Sharks where he will team up with a number of familiar faces.
The physical No 8, who can also play blindside flanker, formerly played with New Zealand provincial side North Harbour and has scored two tries in eight internationals.
“I’ve played against a few of the squad – Nasi Manu back in New Zealand and Will Helu in the Premiership, though I’ve also played with him in the Tongan team,” he said.
“Of course I’ve played alongside Fowlesy [Nathan Fowles] at Sale and also with Phil Burleigh in a Chiefs development side.
“The move will be a great adventure for me and my family and I’m looking forward to getting involved.”
Edinburgh Rugby head coach Alan Solomons said: “We are delighted that Vili has signed for the club. He is a big, powerful ball carrier with international experience.
“I have no doubt that he will add huge value to the team and look forward to working with him.”
Meanwhile, Scotland international Hugh Blake has returned to New Zealand on loan from Glasgow.
The 23-year-old flanker will play with Bay of Plenty Steamers in the Mitre Cup in a loan spell which lasts until the end of October.
The former New Zealand Under-20 international and Otago player told his new club’s website: “It’s great to come back, especially with my mum’s family still being based here, so there is plenty of support.”