Tying the 23-year-old down on an extended deal is a significant boost for the capital club who are losing fellow winger Duhan van der Merwe to Worcester Warriors in the summer.
Graham is one of the brightest home-reared talents in Scottish rugby and has scored 17 tries in 39 appearances for Edinburgh where he has been potent attacking threat for the club over the past three seasons.
A pacy and elusive runner, he has been capped 19 times by Scotland and has scored nine international tries, an excellent strike rate at Test level.
He is currently sidelined after having surgery to repair a long-standing shoulder issue which is likely to see him miss Scotland’s summer tour to Georgia and Romania.
Graham, who came through the ranks at his hometown club Hawick, won his last cap in the Six Nations win over France in Paris in March.
Edinburgh have not revealed the length of the new contract, saying only that it was for “several years”.
Graham said: “I’m delighted to extend my time with Edinburgh. I wouldn’t want to be anywhere else.
“I’m living the dream, playing the sport I love for club and country. Hopefully I can continue to improve my game and really kick on.
“So much of what I’ve enjoyed has come in my time at Edinburgh and really think this is the right place for me to continue to work hard, get better and challenge for silverware with a good group of boys.
“The fact that we’ll be doing that in a new stadium we’ll soon be calling ‘home’ makes this a really exciting time.”
Richard Cockerill, the Edinburgh coach, added: “Darcy is a player of undeniable quality and finishing ability. He’s a textbook example for all the young Scottish kids out there of how the game remains one for all shapes and sizes and that, through hard work, you can make to the top of your game.
“He joined our academy from Hawick, which we all know is a town and club famous for producing quality rugby players and has developed – and continues to develop – his game really nicely.
“His speed, footwork and skillset make him nightmare to defend against.”