Tofilau was invited to train with Edinburgh and showed off his potential in the Melrose Sevens, where he scored a try in the final as they won the tournament, which prompted coach Andy Solomons to hand him a deal.
"I'm really excited to be involved at the club and I'm grateful to the coaches for putting faith in me. Hopefully I can return the favour in the way I train and play," he said.
"I am excited and a little bit nervous for pre-season, but I'm looking forward to getting started.
"It's going to be tough, but I know it's all going to help me adapt to the environment and push me to achieve my goals and dreams."
Tofilau becomes the latest Edinburgh signing, joining the likes of Kevin Bryce and Nick Beavon, as the club looks to complete business early.
Solomons currently has Phil Burleigh, Chris Dean and Junior Rasolea to choose from at centre, but he remains convinced Tofilau will make an immediate impact.
"We are delighted to welcome Sasa to the club," he said.
"He is a talented young player, who has represented Australia at under 20 level.
"I have no doubt he will make his mark at Edinburgh and look forward to working with him."
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