Now in his second season with the club, the winger has cemented his place in the starting XV, scoring seven tries in 12 appearances in both the Guinness PRO14 and Heineken Champions Cup.
The Hawick flyer was rewarded for his form earlier this season when Scotland Head Coach Gregor Townsend called him up for his international debut against Wales in the 2018 Autumn Tests – becoming the 1098th player to represent Scotland.
On extending his stay in the capital, Graham, said: “I’m absolutely buzzing to be staying at Edinburgh for the next two years. The club is building towards something very special, on and off the field, and I can’t wait to be a part of it moving forward.
“I’ve grown up watching Edinburgh and I never thought in my wildest dreams that I’d be going into my third season with the club. I’m loving it here and I can’t wait to see how much I can push myself and learn over the next two seasons and beyond.”
Head Coach Richard Cockerill added: “Darcy is a really important part of this team, so I’m delighted that he has chosen to commit his immediate future to Edinburgh.
“His attitude and hard work ethic are an example to anyone looking to make a name for themselves in the modern professional game. I’m excited to see him progress further in the years ahead.”
At just 17-years-old, Graham helped lead his hometown team, Hawick RFC, to the Scottish Cup Final against Boroughmuir in 2015, whilst he proved to be a show-stopping talent on the Borders Sevens circuit.
Following impressive performances for Scotland under-18 and Hawick, Graham was inducted into the Fosroc Scottish Rugby Academy, based in the Borders.
The winger was named in the Scotland U20 squad for the 2016 Six Nations, where he made his debut in the 24-6 win over England in the Championship opener.
Graham signed his first professional deal with Edinburgh in the summer of 2017 and made a try-scoring debut in the 50-20 European Challenge Cup win over London Irish in December that same year.
Now a Scotland international, Graham has played a vital role in Edinburgh’s run to the Heineken Champions Cup Quarter-Finals, scoring the winning try in last month’s crucial pool stage victory over Montpellier at BT Murrayfield.