Vue offered to sell the cinemas to remedy the Office of Fair Trading's competition concerns following the acquisition of Apollo Cinemas.
Pre-deal, Vue ran 68 cinemas in the UK, adding 14, as well as two opportunities to open more in the UK, with the Apollo transaction.
The OFT's investigation found the acquisition raised competition concerns in four local areas in England and Wales where there was a risk that the cinemas could raise prices, or reduce film choice and quality of service to customers.
Vue has offered to sell all four Apollo cinemas to Reel in Fareham, Port Talbot, Morecambe and Burnley.
'The OFT was concerned that, as a result of Vue's acquisition of Apollo, cinema goers in four local areas could face higher prices and a reduction in choice," said Amelia Fletcher, OFT chief economist and decision maker in this case.
"The OFT believes that the sale of all Apollo cinemas in these areas to Reel will now ensure there continues to be effective competition in these areas."
The government watchdog will not now refer the Vue/Apollo acquisition to the Competition Commission.
Reel Cinemas already operates 12 cinemas, including five across the Midlands in Bridgnorth, Grantham, Halesowen, Ilkeston and Kidderminster.