The 22-year-old – who can also operate in the back row – joins fellow academy product Jamie Ritchie in this week committing his long-term future to the club.
On penning a new deal, Carmichael said: “I’m really excited to extend my time in Edinburgh. I’ve loved every minute here and it’s an exciting time to be part of the club.
“We’ve enjoyed a great start to season and I’m looking forward to putting my hand up for selection moving forward.”
Edinburgh head coach Richard Cockerill, added: “Lewis is a talented young player with bags of potential. We’re delighted that he’s chosen to stay here in Edinburgh to be part of what we’re building on and off the field.”
A product of nearby North Berwick High School, Carmichael represented Edinburgh at U17 and U18 levels before progressing into the Scotland age-grade set-up.
After making his U20 debut against Ireland in January 2014, the second-row would play a vital role in the age-grade side’s success during the 2015 Six Nations Championship – a tournament in which he scooped two man-of-the-match awards.
The 22-year-old won the Premiership title with Melrose before making his Edinburgh debut off the bench against Munster at Thomond Park during last season’s PRO12 season.
The lock joined Super Rugby franchise Western Force on a loan-deal in February 2017 as part of his long-term development plan, and was called up to join Gregor Townsend’s squad for the final two legs of his maiden summer tour as Scotland head coach.
Carmichael has made 21 appearances for the club and scored a try during Edinburgh’s 78-0 European Challenge Cup victory over Krasny Yar on Saturday.