The channel, which is available on both Sky and Virgin TV, reaches 4 million people a month.
Quiet Storm will be briefed with creating an overall campaign that will build on the brand as well as fast turn around executions highlighting up-coming films.
Sparrowhawk Media, which also owns the Hallmark Channel, features movies from the biggest distributors, including Sony, MGM, Paramount and Fox.
Maya Bhose, the marketing director at Sparrowhawk, said: “Movies 24 has already firmly established a great audience but now is the right time to take the channel to the next stage. Quiet Storm completely understands the value of engaging with viewers and building relationships with them and I’m delighted to be working on this project with the Quiet Storm team.”