The tennis greats linked up for the Serb's Australian Open campaign and the 24-time major champion has confirmed that the pair will carry on working together through the clay court season.
Djokovic told the ATP Tour's media channel: "We had a chat the day after I finished [the Australian Open], we reflected on the period we spent together.
"We agreed he was going to take some time and think, speak with his family members and see if he decides to keep working.
"I expressed my desire to continue the collaboration with him, so I am really glad he did accept.
"It is indefinite in terms of how long we are going to work together, but we agreed most likely in the States and some clay court tournaments. We will see how it goes after that."
Djokovic reached the semi-finals at the Australian Open under Murray's guidance before being forced to retire through injury and has hailed the Brit's approach to the arrangement.
The former world number one said: "He knows exactly what we need to do tactically - the evolution of my game and what needs to be improved.
"He has a positive approach and has handled the whole pressure very well as it is a completely different situation from being there as a player.
"He has been terrific with all the other team members and while it was unfortunate the way the Australian Open finished with injury, we had a great run."
Murray previously recalled how he was caught off-guard by Djokovic's proposal.
The three-time Grand Slam winner said: "I was on the 17th hole of the golf course and the guy I was playing with said to me, ‘Do you know what’s next?' I was like, ‘No, not really’.
"He said, ‘Do you have any plans to do any coaching?' And I said, ‘Honestly, I can’t think of anything worse to do right now’.
"And then 30 minutes later I was in the car and I called Novak, and then we had a conversation, and he asked if I would be interested in helping, which I obviously wasn’t expecting."