Visitors from the US, Europe and Australia have already descended on the Halifax attraction to view the dresses, suits and accessories worn by the likes of Suranne Jones and Sophie Rundle in the period drama, which has been one of the BBC's most successful programmes of the year.
Many are now including the museum on their own 'Anne Lister trail' - an itinerary which also features her ancestral home, Shibden Hall, and several locations used for filming.
Gentleman Jack concluded last Sunday and told the story of 19th-century Halifax landowner Anne and her relationship with same-sex partner and fellow heiress Ann Walker.
The Bankfield curators have been loaned the costumes by Lookout Point Productions, and designer Tom Pye has put the 'finishing touches' to the displays, which opened to the public on Friday morning.
The garments have been in storage at the museum in Boothtown - itself a grand mansion once owned by mill baron and MP Edward Akroyd - for several months, with strict instructions that they could not be unveiled until the end of the series.
Elinor Camille-Wood, head curator at both Bankfield and Shibden, believes the exhibition could be the most popular in the museum's 120-year history.
"We are so lucky to have got the costumes - we've had them for weeks, but there was a final episode embargo.
"The reaction has been amazing. We've had so many messages of support from all over the world, and our social media accounts have gone mad. People are spending a whole day at Shibden and Bankfield and exploring the wider area too, which has so much to offer.
"We've had visitors from the US, Germany, France, Australia - a lady from the US rang us up and asked where the nearest airport was as soon as she heard about the exhibition! It shows the depth of passion there is for Anne Lister and Gentleman Jack.
"We knew it would be popular as it's such a powerful story and people are so inspired by it."
On display are four of Ann Walker's outfits, including her pink and blue dresses and the checked frock she wears when she first kisses Anne Lister, whose top hat and travelling outfits are also available to view, as well as the engagement rings worn by both women. There are 12 mannequins in total, some showcasing costumes worn by male characters.
"We don't have Anne's long black coat, but we are planning another exhibition of outfits designed by another company, so we hope to have it then."
The museum is also home to a fashion gallery that features a collection of original clothing from the 1830s.
Elinor is revelling in Halifax's moment in the sun, signposting Gentleman Jack fans to locations scattered all over 'Callywood'.
"They are astounded that Shibden is still there and that it is cared for so well. They love the mix of country and town here. They say how lovely and welcoming the staff are and it's given us a real boost.
"We've also had a lot of local people come who said they hadn't visited since childhood."
Among the international contingent crowding into Bankfield for the launch of the exhibition were two fans from Belgium and America.
English teacher Janne Monballiu, from Antwerp, was already aware of Anne Lister but has enjoyed exploring Yorkshire and following in her footsteps.
"I'm a big fan of Sally Wainwright's work and it's culminated in such a brilliant series. I have a lot in common with Anne Lister and the show just clicked with me. It's the first time I've been to Yorkshire and I love the area - there is nothing to compare it to in Belgium.
"I've been up to Shibden every day since I got here to walk around, and I love the exhibition - the attention to detail is just amazing."
Shantel Smith, from North Carolina, is such huge Anne Lister fan that she has booked tickets for every talk and event she can find about Halifax's most famous daughter.
"I came to London in May and thought, since it's so close I might as well go up to Halifax. I love it here. I've been to all the events with authors and historians - anything that's on the calendar. I've driven all over Yorkshire looking at the locations from the series.
"Anne's diaries have really lasted the test of time - they are so detailed. She's really intelligent, although she has some quite conservative views so I'm not sure we'd be friends today! It's fascinating to be able to connect her writing to real history, it's not just fiction. The TV show has been amazing - before it was shown, I didn't know she existed."
The Gentleman Jack costume exhibition runs until October at the Bankfield Museum, Halifax. Entry is free.