Murray broke his major duck after teaming up with Lendl two years ago and went on to end the 77-year search for a British men's winner of the Wimbledon singles title.
Lendl, whom it is believed could not give his full attention to Murray's schedule due to other commitments in the sport, stressed the parting of the ways was amicable.
Lendl said: "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.
"Working with Andy over the last two years has been a fantastic experience for me. He is a first-class guy.
"Having helped him achieve his goal of winning major titles, I feel like 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 believes the success of his partnership with Lendl will stand him in good stead for more major success.
Mirroring Lendl's own playing career, Murray had lost his first four grand slam finals before teaming up with the Czech and making his dramatic breakthrough.
Murray said: "I'm eternally grateful to Ivan for all his hard work over the past two years - the most successful of my career so far.
"As a team, we've learned a lot and it will definitely be of benefit in the future. I'll take some time with the team to consider the next steps and how we progress from here."
Murray's difficult start to the new season is not thought to have had any bearing on Lendl's departure.
The Scot has slipped to sixth in the world rankings as he continues to recover from the back surgery he underwent at the end of last year.
He will now head into the defence of his Sony Ericsson Open title in Miami having failed to go beyond the semi-finals in any tournament so far this year, and having suffered a shock straight-sets loss to Milos Raonic in the last 16 in Indian Wells earlier this month.