The reformed partnership will start from Monday at the grasscourt Aegon Championships at Queen's Club, the Wimbledon warm-up event, with the Scot hoping it will be both successful and lasting.
"Provided everything’s good, it will hopefully go on for a long time," Murray said after announcing the move on Sunday.
Czech-born Lendl, 56, was world number one in the 1980s and won eight Grand Slam singles titles -- three French Opens, three U.S. Opens and two Australian Opens.
The two parted in March 2014 after two years during which Murray won the 2012 Olympic gold, the 2012 U.S. Open and the 2013 Wimbledon title.
Murray, who reached his first French Open final this month, has not added to his two grand slam titles since their separation.
"I think the most successful period of my career was while I was working with Ivan. I know what he can offer," he said.
"The experiences he had, I think psychologically he helped me in the major competitions and they're obviously the events I'm trying to win and am competing for.
"I hope he can bring that same experience and those same benefits that he did last time."
The 29-year-old, who has former British player Jamie Delgado as his full-time coach, worked with French coach and former Wimbledon women's champion Amelie Mauresmo until May.
Mauresmo helped guide the Scot to seven titles and two Australian Open finals.
Lendl, who has been working in the United States with the USTA Player Development programme, said he had enjoyed working with Murray before and looked forward to doing so again.
"Andy and I have always stayed in contact so it should be fun to be part of his team again," he added in a statement.
Murray, going for his fifth Queen's title, took five days off after his French Open defeat to Novak Djokovic before practising again on Saturday.
"I'd never done that well on clay before so I needed to let my body rest and recover a little bit before I started practising on the grass again," he said.
(Reporting by Alan Baldwin, editing by Ian Chadband)
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