The hub was one of 32 new sites to open nationwide today, marking a ramped up roll-out of Covid jabs.
Vaccines will be delivered from the Tipton Road-based site over the next several months as the NHS works down the age categories.
The first cohort of patients will be those aged over 80 and living within a 45 minute drive of the museum in Dudley.
The borough's council leader Patrick Harley hailed the opening of the hub, telling the Express & Star: "It is absolutely brilliant.
"This is possibly the last piece of the jigsaw that we need to combat the virus once and for all.
"A lot of our residents in the borough and further afield would have been to the museum many times.
"It is quite a nervous time for people coming to get their injections, coming here may well place them at ease."
It will be the Oxford-AstraZeneca vaccine that will be administered to patients at the museum, rather than Pfizer.
Ruckie Kahlon, chief pharmacist at the Dudley NHS Trust, said: "That is how it has been allocated to us by the national teams.
"[We have] opened the first vaccination hub in the Black Country and west Birmingham [at the museum].
"We are aiming towards [vaccinating]1,000 people per day."
Frontline health workers have been redeployed to carry out the vaccinations.
They were the first people to be given jabs on Monday, ahead of the general public who are expected sometime this week.
Among them was Davinder Manku, a pharmacist at Dudley NHS Trust, who was the very first person to receive a vaccination.
She said: "I feel really privileged to be the first person. It has taken a lot of work to set everything up here."
Bosses at the museum were approached by the NHS several months ago in utilising the site for a vaccination hub.
The jabs will be administered to people in rooms located within the main building, along a corridor to the left of main reception.
Natasha Eden, chief operating officer at the museum, said: "We feel very privileged to be able to host the NHS here during this period, because we can't be open, as you can imagine, as a normal museum, and for most of last year as well.
"The opportunity to work with our community in a different way is a real privilege for us."
Letters have been sent out inviting people for vaccinations.
People have been asked not contact the NHS about jabs but wait for their invites.
Dudley North MP Marco Longhi, whose constituency covers the museum, said he was delight to see the museum opening.
Mr Longhi said: "Having this as a super hub, it means we are going to accelerate even further the number of vaccines that we are carrying out, not just in Dudley but contributing to that massive effort nationally.
"I am so proud to be part of the whole machine that is making this happen."
Mike Wood, the MP for Dudley South, added: "It has been fantastic seeing how well organised everything is and the great work that has been done by the doctors, nurses, pharmacists, other staff and volunteers who have worked so hard to set up this brilliant facility.
"This site will be doing a thousand vaccines per day, meaning they can offer seven thousand vaccines each week to the most clinically vulnerable people.
"This is on top of all the other vaccination centres around the borough – making sure that all of those on the priority list can be vaccinated as quickly as possible."