The agency picked up the business after a four-way pitch against three unknown shops.
The incumbent on the account, Lowe Athens, decided not to repitch. Agency Assessments handled the review.
My Agency will be briefed with the task of defining the brand's overall strategic direction around the globe.
It will also be responsible for creating global campaigns, which will continue the existing "Try a different angle" strategy that was launched back in 2005.
Neil Brettell, the global brand director at Grant's, said: "This is a crucial appointment for us since we have ambitious plans for Grant's.
"We were impressed by the passion, commitment and the vision for the brand presented by My Agency; it really gets the need for ways to extend the campaign right across the marketing mix."
My Agency's other accounts include AMD PC processors, London Clubs International and O2's Be broadband.
Grant's is owned by William Grant & Sons, a family owned distillery, which also produces Glenfiddich, The Balvenie and Reyka vodka.