Big-hitting Czech Berdych announced on his Facebook page on Tuesday that he would be working with Vallverdu and thanked former coach Tomas Krupa, who he had worked with since 2009.
Venezuelan Vallverdu worked with Murray for five years, often acting as an assistant coach, before parting company with the Scot last month.
Berdych, who has reached one Grand Slam final -- beaten at Wimbledon in 2010, had previously expressed a desire to appoint eight-times major winner Ivan Lendl, who coached Murray to his first major title in 2012, in the hope that he would take the Czech to the next level.
With Lendl reluctant to commit to a full-time coaching role again, his former coaching partner Vallverdu is seen as the next best option.
"You guys don’t understand how much I relied on Dani," Lendl said of his successful coaching spell working with Vallverdu for Murray.
(Reporting by Sam Holden; editing by Justin Palmer)
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