The sale by the confectioner, whose brands also include Maryland Cookies and Jammie Dodgers, is part of a wider, long-term supply deal with the Swiss chocolate company, which will continue to supply more than 12,000 tonnes of chocolate a year to Burton's.
Barry Callebaut said it will take on the 48 staff currently employed at the Burton's factory in Moreton and continue making chocolate at the site.
The Swiss firm, which trades on the pan-European Stoxx exchange, said the deal will help it expand its manufacturing capability in the UK, which it sees as a growth market for the group.
The deal is expected to close by the end of 2018.
Nick Field, chief executive of Burton's Food, said: "Barry Callebaut shares our passion and motivation for baking the best quality products for our customers and consumers.
"This new partnership, with their larger network and enhanced capabilities, directly supports our intent and commitment to maintain and enhance our industry-leading chocolate biscuit offering."
Barry Callebaut's chief executive, Antoine de Saint-Affrique, added: "This transaction is an excellent example of the power of long-term partnerships and outsourcing.
"It is also a clear sign of our commitment to support the growth of our business in the UK market."
Burton's has been manufacturing chocolate at the site in Moreton since the late 1950s.
Based in Hertfordshire, Burton's traces its roots back to the mid-1800s, when it was founded by George Burton.
Burton's, which now makes Mars-branded products, employs about 2,000 people around the UK at a number of distribution and manufacturing facilities.