Leasing the Chesham House site, which is owned by the National Housing Group, external, will cost the council £8.4m and a further £6.5m to operate the accommodation.
But, the authority said it would be able to recover the latter figure as service charges paid by its tenants.
Labour councillor Keith Darvill said the accommodation would need to be suitable and there had been plenty of examples where commercial property had not been appropriately converted.
However, he said the situation with temporary accommodation in Havering was a “real mess”.
Patrick Odling-Smee, a member of the council’s executive leadership team, said the council would rather not be using a commercial property to accommodate homeless families, but various housing challenges had led them to this situation.
Councillors approved the plan at a cabinet meeting on 11 December.