Italian spirits group Campari is paying €128.2 million for the liqueur brands.
The latest deal is a clear sign that Tullamore Dew Irish whiskey was the key prize for Grant in the package that it originally bought.
Grant has already set up a new marketing office in Dublin to handle the brand.
Campari chief executive Bob Kunze-Concewitz, said: “With Carolans, Frangelico and Irish Mist we add a high quality and profitable business with upside potential and further enhance the group’s premium offering.”
He said the deal would “strengthen our exposure in key international markets including the UK.”