The measure passed by a vote of 18-2 after an earlier motion, which would have deferred the matter until the new school board is sworn in next month, failed.
A delay would have risked killing the $6-million project said Trustee Briony Glassco, as the board debated the deferral.
The seasonal dome will cover the school's large outdoor track area, which runs along Bathurst Street south of Bloor Street West, for four or five months out of the year — providing more space to the school's athletic program. The plans include installing artificial turf.
A similar dome at Monarch Park Collegiate Institute led to an "explosion of school pride" said Glassco.
Area residents have opposed the plan, raising concerns that include the neighbourhood's lack of greenspace and parking.
The board made almost no mention of its recent, internal troubles, which earlier this week led Ontario Education Minister Liz Sandals to order a review of what she described as a "culture of fear" among the staff.
Police were called to a recent meeting of Canada's largest school board amid accusations one trustee held the director of education, Donna Quan, hostage in her office.
The TDSB was also the subject of two external audits which uncovered problems with capital and structural deficits and with trustee expenses.