British No1 Murray, 27, has worked with Vallverdu for five years and Green for seven years.
“We sat down at the end of the season and decided that a change would be best for all of us,” said Murray.
“My off season training and Australian Open preparations have already begun and I am very excited for the new year.
“I thank Jez and Dani for all their hard work over the years and wish them the best for the future.”
Murray looks set to retain Amelie Mauresmo as his head coach after she took the role in March.
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