Director of Fairfax House Peter Brown said the barometer, which dates from 1695, would be checked for damage by a conservator before being put back on display.
Mr Brown praised the North Yorkshire Police investigation which led to the return of the barometer, and confirmed a security review had been launched.
He said: "It is not in too bad a condition on the surface, but we are getting a conservator in to check. The barometer contains mercury and we are having that looked at and we are obviously going to upgrade our security."
The theft was only the second in the 25-year history of the museum, which is the home of the Noel Terry collection of English furniture and clocks. The exact value of the barometer has not been disclosed, although it is believed to be worth several tens of thousands of pounds.
Mr Brown said: "It is still distressing and there are lessons to be learned. We are just so pleased to have got it back. It is such an important part of the Noel Terry collection. It is one of a very small and unique group of barometers made by Daniel Quare."
The barometer was stolen by a visitor who was recorded on closed circuit television cameras at Fairfax House on May 18. He will be sentenced at York Crown Court in July.
Quare's customers included the Royal Family and his work can still be seen in Windsor Castle, the Science Museum and other high-profile venues.
Fairfax House, which was restored by York Civic Trust between 1982 and 1984, was created in 1762 as a dowry for Anne Fairfax, the only surviving chid of Viscount Fairfax.
Update: Woman quizzed over stolen antique