The Scotland under-20 international has put pen to paper on a two-year deal.
Carmichael, who turns 21 next month, has been with Melrose since leaving school and played for the Greenyards side in Saturday’s BT Cup defeat against Heriot’s.
He was awarded a BT Sport Scottish Rugby Academy contract last summer and has now graduated to a pro deal.
Edinburgh head coach Alan Solomons said: “Lewis is a talented young Scottish lock who has made good progress this season and shown that he has what it takes to be a pro player.
“We are pleased that he has decided to remain with us and look forward to continuing to play a role in his development.”
Carmichael said: “I’m a local boy, I grew up in East Lothian and Edinburgh’s the club I‘ve always wanted to be involved in. It’s great that Alan’s seen the potential and has belief in me.”
The Edinburgh-born, former North Berwick HS pupil represented the city of his birth at under-17 and under-18 levels before being drafted into the Scotland under-18 squad, making his debut against England in March 2013.
He moved up to the Scotland under-20 side and scored his first try to help secure a 36-34 victory over Wales in February 2015, and he crossed the line to score Scotland’s sole try in the World Rugby under-20 Championship opener against New Zealand, last June.