The institution bought the five-floor luxury property despite Sir Jim McDonald - Scotland's highest-paid principal - already having use of a grace-and-favour residence in the city.
Staff including lecturers were offered a pay increase of just 1% last year, while dozens of other employees are on zero-hour contracts.
The property is at Park Circus, Glasgow, while the principal's existing residence is an apartment in University House, which is part of the now-closed Jordanhill campus. The Park Circus townhouse is intended to "replace" University House.
Other benefits include underfloor heating in the lower ground floor and "meticulously maintained" private gardens.
The university spent £1,180,000 on the purchase, with another £300,000 being earmarked for "refurbishment".
The University Court, the key decision-making body on campus, approved the finance behind the purchase last May.
A Court minute notes that the existing residence is "no longer suitable" due to Strathclyde no longer using Jordanhill.
Mary Senior, Scotland official at the University and College Union, said: "Staff at Strathclyde University will be stunned by their employers pleading poverty, while buying a luxury townhouse in one of Glasgow's plushest postcodes. Staff in our universities have seen their pay fall in value by 13% over the past five years, while those at the top seem oblivious to the hypocrisy of lining their own pockets."
David Meikle, a Glasgow Tory councillor, said: "The revelation that the university has splashed out over £1m to buy a luxury property for use by the principal and his colleagues is unbelievable."