Strachan won three titles and three domestic cups during his four years in charge of Celtic.
Strachan said: “I have enjoyed my time immensely at Celtic and clearly I will be sad to leave this great club.”
Strachan added on the official Celtic website: “As I have said before, Celtic is a special club, with special supporters.
“There is no club like it and it has been an absolute honour and privilege to be the club’s manager for the past four years.
“We have done all we can to bring success to the club and we were delighted to deliver three SPL titles, other domestic silverware, as well as making some great progress in Europe.
“It is just disappointing that we did not manage the fourth championship.
“However, the players can hold their heads high in terms of what they have done for the club in recent years.
“I would like to thank the Celtic board for all the support they have given me during the past four years, in particular Dermot Desmond, John Reid, Peter Lawwell and former chairman Brian Quinn – I could not have asked for any more support.
“I thank all the players I have worked with at the club and, of course, my backroom team for the backing and assistance which they have given me.
“I thank the fans too for the tremendous support which they have given both myself and the players. I wish Celtic and our supporters nothing but success for the future.”
Celtic chief executive Peter Lawwell said: “Gordon has given everything to the club and worked tirelessly to bring success to Celtic.
“He has achieved so much at both domestic and European levels.
“It has been a pleasure to work closely with Gordon and he leaves the club with all our best wishes.
“We thank Gordon for his commitment and achievements at the club and we also thank our fans for backing us all the way this season.
“Our fans know how to support their club and we will be doing all we can to once again bring back the title to Celtic Park, something which our support deserves.”