The hotel closed on the 26 March before the owners, Signature Living, entered administration.
The property has since been acquired by Eden Grove Properties, saving a number of jobs in the process.
Some 80 bedrooms and suites are now in operation as part of a staggered reopening while Culley’s, the hotel’s bar and restaurant, will also renew its service.
Brain Gamble, operations director of The Coal Exchange and former employee at Signature Living, said: “I am delighted we have been able to work with the administrators to reopen the hotel under new ownership whilst saving 40 jobs in the process.
“We were all devastated when we were forced to close due to COVID-19 and lockdown. We were further dealt a blow whilst being informed that our previous employers had entered administration whilst we were furloughed.”