Last month, Smith, 29, stood down from the Scotland tour of Argentina citing a need for a break.
After considering his options to remain in professional rugby and advance his ambition to add to his 25 Scotland caps, Smith believes his best option is now to seek a fresh start at a new club.
He said: "I've done a bit of soul-searching and I'm very grateful to Edinburgh for all the opportunities that I've enjoyed since I came back to Scotland from the Stoke club in Nelson, New Zealand in 2000.
"But I feel now that a new challenge would be the best thing to give this stage of my rugby career some impetus.
"I'd like to thank Edinburgh and Scottish Rugby for their understanding in agreeing to my request.
"I will leave with many happy memories and pride at playing my part in making Edinburgh, on our day, one of the best teams in the Magners League and an attacking side to be reckoned with in Europe."
After making 167 outings in the black and red jersey, Smith leaves the club as Edinburgh's second leading all-time appearance holder.
Edinburgh chief executive Nic Cartwright thanked the popular prop forward for his dedication to the team over the past eight years; both on and off the pitch.
Cartwright: "We would like to thank Craig for his contribution to the growth of Edinburgh over the past eight years.
"He has played a pivotal role on the pitch and also off the pitch where he has helped us to forge great links with the local rugby public through his community visits.
"We wish him all the very best as he embarks on the next chapter in his playing career."
Edinburgh head coach Andy Robinson echoed those sentiments and said: "Craig is a good team man. I wish him all the best and thank him for his years of service to Edinburgh."
Guinness PRO12
Suite 208, Alexandra House,
The Sweepstakes
Ballsbridge, Dublin 4, Ireland