The 21-year-old Sydney-born playmaker, who qualifies for Scotland through his Ayr-born father, has so far made eight appearances for the club since making the cross-code switch from Sydney Roosters in October 2020.
After pledging his future to Edinburgh, Savala told the club's website: "It's a special moment for myself. This club means a lot to me. I'm so grateful to be in the position I am and to be part of such a competitive squad.
"I'm glad to have found my feet here. I love this place and being a part of the club. This is my home and I'm excited to see what the future holds in the Edinburgh jersey.
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"This is everything I've ever wanted. To be able to stay at the club I love and to call it home is awesome. I've made some good friends here and I'm really grateful for the boys I've got around me."
Head coach Mike Blair is looking forward to seeing Savala continue his development at Edinburgh.
"I'm really excited to see Charlie re-sign," he said. "He's a guy that possesses a lot of natural talent, while he's really popular around the club and brings a brilliant attitude to training every day.
"Charlie's ball playing skills are clear to see. He's got great vision and plays with raw instinct, while he's stepping up to be a real leader in the playing group too.
"What's also impressed me about Charlie is he continues to work hard on those parts of his game that will make him an even better stand-off in the future, like his game management and tactical kicking.
"It's great that Charlie is happy in Edinburgh and we're excited to see how he develops his game alongside the other half-backs at the club."