The practice was selected ahead of five US-based finalists and has been asked to draw up plans for an 'all-new and expanded' home for the museum, which is currently housed on the second floor of the Cleveland Playhouse.
Part of the 3.2ha University Arts and Retail District regeneration programme in the heart of the Ohio city's cultural hub, the $25 million (£13 million) MOCA project will increase the museum's floor space as well as providing new visitor facilities and flexible 'new media' rooms.
Describing FOA's selection, Harriet Warm, MOCA's board president, said: 'We looked at the work of many superb architects.
'Ultimately, we agreed that FOA, with its consistent record of excellence, will create an outstanding design that responds to the museum's need for flexible space and its diverse audiences.
'We also believe that our new building will help to enliven the neighbourhood, which is an important aspect of the district development.'
The international design competition was launched in 2005 and FOA was one of just 30 'emerging talents' interviewed by the museum's Architect Search Task Force.
FOA has become famous for its overseas commissions, including the Yokohama Ferry Terminal which, if it had been built int he EU, observers say would almost certainly have made the Stirling Prize shortlist.
FOA continues British trans-Atlantic success with US art museum win