Ivan and Andy are going to work together in the United States next month.
They will spend several weeks training after the Miami Masters as Murray prepares for the grass court season.
Murray decided to skip the clay court season.
He won two Wimbledon titles, the 2012 US Open and two Olympic gold medals while working with Lendl.
Murray became the world's number one.
He was distraught when they first split after he realized the eight-time Grand Slam champion was not prepared to commit to the number of weeks on tour he required.
Murray won his second Wimbledon title in 2016 and finished the year as the world number one.
The partnership ended in November of the following year, with Murray unable to play much because of his hip injury, which required two operations.
An additional coach will travel with Murray and work with him.
The world number 84 has been without a coach since late last year, when he parted ways with Jamie Delgado.
He had trial periods with both Carril and de Witt.
Stan Wawrinka is due to return to the tour in April, but another of Murray's former coaches is still committed to him.
Murray said last month that he needs a consistent message on the practice court and that he misses his coach.
Murray lost in the second round of the four tournaments he has played after reaching the final of the Sydney International. He was beaten in straight sets by Taro Daniel after an excellent five set win over Nikoloz Basilashvili.
Murray has complained about how poor he has been mentally in recent weeks, something that was helped by the help he received from another former world number one, Ivan Lendl.
After his second spell with Murray, Lendl worked with Alex Zverev for just under a year, but has not been coaching on tour since that partnership ended in July 2019.
Murray will have two months to train and prepare for the grass court season after he gets into the Masters Series events in Indian Wells and Miami.
It looks like Lendl will be by his side on the grass courts of The Queen's Club and Wimbledon in June.