Mark Hunter, Molson Coors chief executive UK and Ireland, believes that Doom Bar has the potential to "become a truly extraordinary brand".
It is thought that the acquisition will not prompt any redundancies across Sharp's Brewery's 80 staff.
The acquisition of Sharp's Brewery follows Molson Coors securing the distribution rights for Corona, the bottled Mexican larger, last year.
The new deal will involve Sharp's Brewery keeping its name and branding, supported by the distribution channels of Molson Coors, which has promised investment in the brand.
Sharp’s Brewery claims to be the largest producer of cask beer in south-west England.
Hunter added: "The Doom Bar brand is modern and progressive. It has a loyal following and excellent reputation among consumers and customers alike.
"We have a wealth of experience with this type of venture and an excellent track record of building brands across all markets. We respect and want to preserve the unique culture of Sharp’s Brewery and the special appeal of their brands to beer drinkers."
"This is a new chapter for Sharp’s Brewery and we are excited to play our part in taking Doom Bar to the next stage of its brand evolution."
Molson Coors employs more than 2,000 people, with Carling, Grolsch and Worthington’s brands in its UK portfolio.