The 27-year-old 'Born This Way' hitmaker treated the 'Chicago Fire' actor, who she has been dating for two years, to a bag designed and signed by artist Damien Hirst, reported Sun online.
The unique backpack is covered in mini-versions of Damien's spot paintings - which are rows of randomly coloured circles - and comes with a gold plated brass feet to rest it on.
"Taylor loves his backpacks so she wanted to get him a real one-of-a-kind - only 12 have been made," a source said.
"She's also arranged for a jet to fly them to Chicago so he can see his family. Gaga knows Taylor takes his birthday really seriously but it's always difficult for her to get him something because he doesn't like fast cars, big houses or smart suits," the source added.