The 2013 Wimbledon champion enjoyed some of his best tennis with the pair in his corner, but after five years with Vallverdu and seven with fitness trainer Green their working relationship has been brought to an end.
"We sat down at the end of the season and decided that a change would be best for all of us," Murray in a statement.
"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."
Vallverdu has been part of Murray's team since 2009 and, working with former coach Ivan Lendl, helped improve the Scot's tactical game in recent years.
Meanwhile, physical conditioning trainer Green is now set to focus on helping the rising stars at the Monte Carlo Tennis Academy.
It means Murray has now removed all of the team that saw him claim two grand slam titles, having replaced Lendl with Amelie Mauresmo in June.