Cineworld said it will "reluctantly" sell Picturehouse cinemas in Aberdeen and Bury St Edmunds, and is weighing up whether to sell a Cineworld or Picturehouse outlet in Cambridge.
The Competition Commission confirmed a ruling in August that its acquisition may mean a "substantial lessening of competition" in these areas.
Cineworld, which has 78 UK cinemas mainly in out-of-town locations, bought the chain of 21 small, city centre cinemas in December for £47 million.
Chief executive Stephen Wiener said Cineworld was "very disappointed" by the final decision.
"We will be selling these cinemas as going concerns and will be supporting our affected cinema teams through the sale," he said.
Commission deputy chairman Alasdair Smith said Cineworld and Picturehouse are in direct competition, with overlapping audiences and screenings.
He said the disposals to a rival will "restore competition in these areas and protect customers' interests".
The Commission said any buyer must continue running the outlets as cinemas and demonstrate "appropriate expertise and experience" to do so.
Analysts at Panmure Gordon said Cineworld is likely to sell the three cinemas for about £7 million in the coming months, adding the disposals will reduce its profits next year.