It bought the five-floor luxury property in Park Circus - one of the city's most exclusive streets - for Sir Jim McDonald, despite him already having use of a residence in another part of the city.
The existing apartment is in University House at the Jordanhill Campus, which was closed by Strathclyde but still belongs to the university.
They claim the Park Circus house will "replace" University House.
But politicians and senior trade unionists condemned the decision.
Staff including lecturers at Strathclyde were offered a pay increase of just 1% last year as a result of the squeeze on public sector spending.
Mary Senior, Scotland official at the University and College Union, said staff at Strathclyde would be "stunned" by their employers pleading poverty while buying a luxury townhouse.
Glasgow City councillor David Meikle dubbed the spend "unbelievable."
A Strathclyde spokeswoman said as well as living accommodation for the principal it will be used for "corporate events and business engagements."