The promotion takes over the deal previously held by EE and Orange.
Meerkat Movies was developed in partnership with Cinema First and is available for new comparethemarket.com customers from 3 April.
Barry Jenkins OBE, the chairman at Cinema First, said: "This deal represents a meeting of minds. Cinema First exists to persuade more people to go to the cinema, whilst comparethemarket.com has realised the potential to tap into the big screen experience as a loyalty programme, to reward their existing customers and attract new ones."
To take up the deal, people will need to buy a product through comparethemarket.com. Existing customers can make use of the promotion now.
Mark Vile, the marketing director at comparethemarket.com, said: "This is the biggest step change for the brand since launching the Meerkat Toy Collection in July 2011 and signals our commitment to rewarding customer loyalty.
"We strive to make comparing and switching as easy and straight forward for customers as possible.
"Meerkat Movies brings this approach to the world of entertainment, offering the magic of the movies for less every Tuesday or Wednesday."