A council spokesperson said: “A recent inspection by us, highlighted urgent work that needed carrying out to keep the buildings open.”
At the Laing, the public lift needs improved wheelchair access while the goods lift will be moved.
“Both the Laing Art Gallery and Discovery Museum are among the city’s finest free cultural assets and are increasingly popular among visitors,” the spokesperson added.
“This [work] will keep them safe for visitors and compliant with legislation while safeguarding their futures.”
Significant restoration work recently began at the Discovery Museum, based in the Grade II listed Blandford House on Blandford Square.
There have long been concerns about the state of the building, which houses treasures such as Charles Parsons’ Turbinia – the first ship to be powered by steam turbines and once the fastest vessel in the world.
Bosses warned in 2022 the venue was in a “serious state of decline”, according to the Local Democracy Reporting Service.
More than £3m in government funding was secured to replace the roof, with work scheduled to be completed by spring next year.