The partnership produced last year's Wimbledon title, the 2012 US Open and an Olympic gold medal.
But the pair have now parted company after two years.
In a joint statement, it appeared Czech-born Lendl, an eight-time Grand Slam champion, may have been the instigator of the split.
"Working with Andy over the last two years has been a fantastic experience for me", said the 54-year-old, who is rated one of the world's all-time great players.
"He is a first class guy. Having helped him achieve his goal of winning major titles, I feel it is time for me to concentrate on some of my own projects moving forward, including playing more events around the world, which I am really enjoying."
Murray, who is now ranked as the world's sixth best tennis player, teamed up with US-based Lendl in December 2011 with the aim of bringing the "experience and knowledge that few others have, particularly in major tournaments".
The Scots star, who has been making a tennis tour comeback after back surgery six months ago, added yesterday: "I am eternally grateful to Ivan for all his hard work over the past two years, the most successful of my career so far.
"I will take some time with the team to consider the next steps and how we progress from here."
There were no signs of the split last week when, after a recent dip in form, Murray insisted things would be no different if Lendl had been with him more during training.
That came just before he was knocked out of the BNP Paribas Open in Indian Wells in the fourth round to the world No 12 Milos Raonic, from Canada.
Murray admitted it was "not good enough", citing one of the reasons as a lack of confidence.
Twelve days previously, after being beaten in the semi-finals of the Acapulco Open by the world's 19th ranked player, Grigor Dimitrov, he sent a message on social networking site Twitter to calm fears about his performances.
He replied to a subsequent message from one fan expressing how he was "very concerned" over his form, saying: "Don't be ... I'm very close to being back to my best."
Before yesterday's announcement, Lendl, who had not travelled to the last tournament, was expected to reunite with Murray next week for the first time since January's Australian Open when the Scot defends his Miami Masters Series title.
Murray had previously worked with the likes of Leon Smith, Mark Petchey, Brad Gilbert, Miles Maclagan and Alex Corretja.
The player had been runner-up in four Grand Slam finals. Only one other man in the Open era, which began in 1968, lost his first four major titles finals, and that was Lendl.
Murray's majors breakthrough came in 2012 when he defeated defending champion Novak Djokovic in the US Open final at Flushing Meadows to win his first Grand Slam singles title.
He then ended a 77-year wait for a British men's singles champion at Wimbledon last summer with a memorable victory against the same player.
Lendl has recently played exhibitions in Kansas City, Oklahoma City, Nashville, Charlotte and London and given coaching clinics, as well as opening new courts in Bluffton, South Carolina, at the Ivan Lendl Junior Tennis Academy.
The coach added: "I will always be in Andy's corner and wish him nothing but great success as he, too, goes into a new phase of his career."