The Zoning Board of Appeal on Tuesday approved plans by the Martin Richard Foundation and the Boys & Girls Clubs of Dorchester for a three-story field house on Mt. Vernon Street in Dorchester that will include everything from basketball courts and running tracks to an auditorium and cafeteria.

The 75,000-square-foot Martin Richard Dorchester Field House , at 301 Mt. Vernon St., on land leased from Boston Public Schools. It would be open during school days to students from the neighboring McCormack and Devers schools, then open to members and the public in the evenings and weekends.

Bill Richard, president of the Martin Richard Foundation - named for his son, who died in the 2013 Boston Marathon bombings - said the new facility will be provide recreational and athletic opportunities for a wide range of people - and will include quiet areas for children who might not do well with loud sounds from basketball courts, tracks that could be used for walking by senior citizens and an auditorium for theater and other performances. A cafe will provide sustenance for people spending a day there.

Other facilities will include indoor fields, training rooms, classrooms, a teaching kitchen, offices and conference rooms.

"This is a pretty exciting project, board Chairman Mark Erlich said. The board voted unanimously in favor, although board member Eric Robinson abstained, because his architectural firm, RODE Architects, designed the building.

The BPDA board approved the proposal in March.

Dorchester field house filings.