The archives, based inside Smethwick Library, in High Street, will see weekly hours reduced from 34 to 24 – with the service also being closed on a Tuesday.
Campaigners say that the reductions were 'unfortunate' but the only way to ensure that the service remained open.
Dr Terry Daniels, who is chairman of the Friends of Sandwell Archives group, said: "It is a shame that this had to happen, but at least it is staying open.
"We hope that by the hours being cut but the facility remaining open that there may be scope for hours to be extended again in the future.
"The sad thing is that the place could disappear and not reopen so reducing the hours are our only option. It is the lesser of two evils.
"We are reluctantly accepting it."
The service currently opens 9.30am to 5.30pm on Monday, Wednesday and Friday, 9.30 to 1.30pm on Tuesday, 10am to 4pm on Saturday and is closes its doors on a Thursday.
The new opening hours will now be 10am to 4pm Monday, Wednesday, Friday and Saturday, with closure on a Tuesday and Thursday.
Councillor Syeda Khatun, cabinet member for leisure and the voluntary sector, said that material available at the library would still be able to be accessed online. She explained: "We hope the altered hours won't disrupt too many people, as they are still longer than in many records offices.
"Much of the material we have at the archives is available online.
"It can be accessed wherever and whenever and makes it much easier for people researching our local history and their family records, but of course we still welcome visitors to the centre during these new opening times."
In May last year the council ruled out shutting its library at Hill Top in West Bromwich, Oakham in Tividale, and Langley, Brandhall and Rounds Green libraries, all based Oldbury, following a public consultation. But to help save £700,000 from the library budget over the next two years, they announced plans to attract volunteers to run events and clubs as one way of saving money.
The council has been continuously battling financial pressures over years after receiving up to £120m less in funding from central Government in the six years to 2015/16.