And the work looks set to pave the way for a larger scale investment in all the facilities at Crow Nest Park, similar to the £5.4m restoration of Huddersfield's Greenhead Park.
Kirklees Council's cabinet last week approved an extra £250,000 for the museum refurbishment, which will provide lift access to all floors and improved public toilets.
It will also transform unused and neglected parts of the museum by updating the wiring and providing IT facilities.
The money has been allocated from the council's culture and leisure budget and will be added to £150,000 already set aside in the council's Disability Discrimination Act budget.
The improvements will make the museum more accessible to people with disabilities.
The council had received complaints from members of the public that the museum's upper floors were inaccessible to wheelchair users.
Coun Khizar Iqbal, cabinet member for stronger and safer communities, said: "Dewsbury Museum is an excellent museum, but unfortunately there is limited access to the upper floors for some people.
"The extension, installation of the lift and other facilities, will improve this museum and increase usage.
"It is already popular, with 35,000 people a year visiting the exhibits, and it will now be accessible to more ensuring improved user satisfaction and fewer customer complaints."
And the council has now set aside money to develop a plan to restore the whole park.
Last year, a £5.4m regeneration of Huddersfield's Greenhead Park was given the go-ahead, £3.7m of which was from the Heritage Lottery Fund.
The council hopes to put together a similar bid for funding for Crow Nest Park.