The decision follows a competitive pitch, after a review was called last year.
UM will deliver customised media buying and planning services for Coach across nine markets in the Americas and Asia.
Carlos Becil, chief marketing officer at Coach, said: "We look forward to working with UM as our media agency of record. We are excited to see the media integration and creativity that they can bring in support of our global brand transformation."
Daryl Lee, global chief executive at UM, said: "Coach is an iconic American brand with a rich heritage of craftsmanship. Our markets around the world are keen to bring the next level of integrated planning and digital and data innovation to Coach."
The win follows a series of others for UM that include Fitbit, Hulu and Accenture. Existing clients include BMW, Johnson & Johnson, Coca-Cola and Fiat Chrysler Automobiles.