The higher education body bought the five-floor luxury property despite Sir Jim McDonald - the highest-paid principal in Scotland - already having use of a grace-and-favour residence in another part of the city.
Politicians and a senior trade unionist condemned the decision last night.
In common with all universities, Strathclyde has kept a grip on costs due to the squeeze on public sector spending.
Staff including lecturers were offered a pay increase of just 1% last year, while dozens of other employees are on zero-hour contracts.
However, the university found enough money in December to buy a property in Glasgow's Park Circus - one of the city's most exclusive streets.
The principal's existing residence is an apartment in University House, which is part of the institution's Jordanhill campus.
The campus was closed by Strathclyde but it still belongs to the university, which hopes to dispose of the site in the long term.
The Park Circus townhouse is intended to "replace" University House.
According to its floorplan, the house boasts three offices, four bedrooms, two bathrooms, a dining room, drawing room, "show" room, workshop, study and two sitting rooms.
The ground floor features a "broad sweeping staircase", twin Corinthian pillars and a marble fireplace which, the advertising blurb notes, "indicate the scale and grandeur of the house".
It also boasts fitted bookshelves, cabling for home cinema, solid granite worktops and a pantry.
Other benefits include underfloor heating in the lower ground floor and "meticulously maintained" private gardens.
The university spent £1,180,000 on the property, with another £300,000 being earmarked last year for "refurbishment".
The University Court, the key decision-making body on campus, approved the finance behind the purchase last May.
A Court minute stated: "The chief operating officer introduced a proposal to acquire a property to replace the University House situated on the Jordanhill campus."
The minute noted that the existing residence was "no longer suitable" due to the institution's move away from Jordanhill.
It added: "Members commented that the university should be clear in explaining the cost of the property and the primary use of the property for hosting university business as appropriate."
The Court approved "the acquisition of a property up to a maximum value of £1.25m with a maximum total expenditure of £1.5m including refurbishment costs".
According to the minute, McDonald was present at the sign-off meeting, as was former university chancellor Lord Hope, former Scottish Enterprise chief executive Dr Jack Perry, the Court's current treasurer, and Labour councillor Stephen Curran.
McDonald, who took up the post in 2009, received a 5% pay rise in 2012-13 and earns £262,500 a year.
His salary is more than £100,000 above the pay that First Minister Alex Salmond receives.
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 and splashing out on pet projects, such as this million-pound property.
"A recent glut of embarrassing stories over principals' pay and perks have made a mockery of any suggestions that we are all in this together."
David Meikle, a Conservative Glasgow 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.
"People will be rightly outraged by this extravagance at a time of public spending restraint. It is also pretty insensitive of the university to do this when staff are getting a 1% pay rise."
Green MSP Patrick Harvie said: "Splashing so much cash on such a grand piece of property shows how ridiculously out of touch the university management is.
"The principal is supposed to lead an academic community; he's not the CEO of a multinational corporation."
A spokeswoman for the university said: "The university purchased the property in Park Circus to replace an existing property at Jordanhill. The property will be used for corporate events and business engagements. The property also has living accommodation for the principal when he is in Glasgow. The purchase will enhance the university's property portfolio and be a long-term investment for Strathclyde."