The 20-year-old from Dumfries-shire made his breakthrough last season, coming on as a late substitute for his Edinburgh debut in the Guinness Pro14 game against Munster at BT Murrayfield.
He scored his first try for the club in the Rainbow Cup win over Zebre at home in April.
He played at outside centre in the away win over Dragons in the United Rugby Championship this season and retained his place for the home victory over Benetton the following week.
A product of the Scottish Rugby academy, Currie is a former Scotland Under-20 international and has played in Super6 for Watsonians.
Edinburgh coach Mike Blair told the club’s website: “We’re delighted to see Matt sign his first pro deal with the club. He’s an exciting young talent and he works incredibly hard in training every day to progress and improve his game.
"He's an impressive young man who has already shown considerable leadership qualities in his short time with the senior squad.
“It’s brilliant to see guys progress and graduate from the Academy. It’s a testament to the good work that is being done from the ground up at local clubs and schools like Dumfries and Merchiston Castle, and within the FOSROC Scottish Rugby Academy.
“Matt is still young, and has a lot of room to grow, however he’s already helping drive competition within his positional group. He’s in a brilliant place to improve his craft, while learning from senior players like Mark Bennett and James Lang.”
Currie said: “I want to keep improving my game and push for minutes on the pitch. We possess a really strong squad and a great coaching set up, so I’m in a really good place to achieve my goals.
“Working with Mike [Blair] has been great, he’s really big into making a club environment and there’s a great vibe around the team at the moment.”