The fourth-ranked Briton will begin working with the Czech-born Lendl as he prepares for the Australian Open, which starts on Jan. 16.
"It was important to me that any new person joining my team was able to add fresh insight," Murray said in a statement. "Ivan's impact on the game is unquestionable and he brings experience and knowledge that few others have, particularly in major tournaments. I look forward to working with him going forward."
The 24-year-old Murray spent all of last season ranked in the top four but still ended it without a first grand slam title.
"I am really excited to have the opportunity to work with Andy," Lendl said. "He is a unique talent and I look forward to trying to help him reach his goals."
The Scot reached the Australian Open final and the semifinals of the other three grand slams last season. He has lost in two other major finals, at the Australian Open in 2010 and the U.S. Open in 2008.
Murray's manager, "American Idol" creator Simon Fuller, hopes that "having a champion like Lendl join his team will help him achieve his ultimate ambitions."