The tapestry has been returned to the Burrell Collection
The 16th century tapestry was found in a litter bin in the city at the weekend after an anonymous tip-off to police.
The 2ft tall tapestry, entitled the Buzzard, was stolen from the museum in Pollok Park, Glasgow, last March.
Police suspected an opportunist thief and despite its £40,000 price tag, thought it unlikely that anyone would be able to sell it on.
On Saturday, Strathclyde Police received an anonymous phone call telling them the tapestry was in a bin in Alexandra Parade.
It was then returned to the Burrell Collection where curators have been examining it for any sign of damage.
Curator Hariet Woolmore said the tapestry had not suffered any permanent damage.
"It doesn't appear to have sustained any great damage and we know it was damp when it was found," she said.
"It is wrinkled and it looks as if it has been folded."
Security measures
Security at the Burrell Collection will be stepped up in light of the theft and the director of Glasgow Museums said it was a fine balancing act between access and security within museums in the city.
Mark O'Neill said: "Security is always a balance of access and prevention of theft.
"We welcome over 3 million visitors to Glasgow museums every year and they can see not only our objects but also our security systems.
"But the council is investing over £400,000 in the next year in museum security so we are very confident that the best value review of security will deliver major improvements."
A police spokeswoman said: "It appears to be in pretty good condition considering it has been missing for over four months."
Glasgow City Council, which owns and runs the museum, said the tapestry was of great value to the city and the people of Glasgow.
The work was acquired by Sir William Burrell in 1938 and was one of the prize exhibits at the opening of the Burrell Collection in 1983.
It depicts a German medieval poem, and shows the buzzard grabbing a ring which an English prince is trying to steal from the finger of a princess, with an inscription calling for God to help with the search.
It is hoped the tapestry will be back on display at the Burrell later this month, protected by a new security system and safely under glass.