It will join a stable of beer brands including Carling, Coors and Doom Bar, but Molson Coors has so far been a minor player in the growing cider market.
It has the distribution rights for increasingly popular flavoured Swedish cider Rekorderlig and in 2013 it launched Carling Cider, but Aspall Cyder is regarded as a more premium brand.
Phil Whitehead, managing director of Molson Coors UK & Ireland, said the company was "looking forward to helping Aspall become the number one premium cyder in the UK".
Barry Chevallier Guild, the chairman of Aspall, said the company had been "in close discussions with Molson Coors for over a year" and believes its acquirer "has the scale and expertise to accelerate our growth in the UK and beyond".
The deal comes ten months after Aspall appointed J Walter Thompson as its first ad agency, giving it a brief to create new positioning and brand platform. The relationship is understood to still be live.
Asked whether Molson Coors would make any immediate changes to Aspall's marketing and what the acquisition means for Carling Cider, a Molson Coors spokesperson said:
"As we begin integrating Aspall with Molson Coors, we will take the time to thoroughly assess the needs of the combined business. Barry and Henry Chevallier Guild will remain very involved in the development of the business going forward in their new capacity as board advisors.
"The team within the Aspall business bring a wealth of knowledge of the premium cider category and expertise in growing premium brands in the UK market. The addition of the Aspall portfolio, alongside our cider range, will contribute to our continuing strong performance and growth within the cider category. The acquisition of Aspall enables Molson Coors UK to offer even greater choice to customers and consumers."