Murray splits from coach Lendl for a third time
The British star won all three of his Grand Slam titles in his first two spells with Lendl and they reunited again in March last year.
But although the Scot regained his place in the top 50 after years of battling to overcome hip problems, he has not achieved the results he wanted, particularly at the biggest tournaments.
"Ivan has been by my side at the biggest moments in my career and I can't thank him enough for all that he's helped me achieve," said Murray, 36.
"He's a unique character who understands what it takes to win and I've learnt an awful lot over the years from him."
Murray won two Wimbledon titles, the 2012 US Open and two Olympic gold medals while working with Lendl.
Lendl's reluctance to travel from his home in the United States has been an issue.
"I will look back with some great memories of the time Andy and I worked together," said eight-time Grand Slam champion Lendl.
"He's as hard a worker as there is and the sport is better because of him. I wish him only the best in the years to come."
Murray, now ranked 42nd in the world, suffered a frustrating first-round defeat against Australia's Alex de Minaur at the recent Paris Masters despite holding a match point, admitting afterwards he is "not enjoying" his tennis.
But he is set to be part of Britain's Davis Cup team for their quarter-final against Serbia in Malaga later this month and it was announced earlier on Friday that he will begin next season at the Brisbane International.
Murray will continue to work with Mark Hilton and Jonny O'Mara.