The singer-turned-actor and 2 Broke Girls star first went public with their romance in October 2014, as they attended The Carousel of Hope Ball in Beverly Hills.
But now E! News reports the pair has made the mutual decision to call time on their relationship.
"It was a mutual breakup," a source told the outlet. "They are still friends and care about each other, but it's not the right time for them now as a couple."
Both Kat and Josh waxed lyrical about each other during their relationship. During an appearance on The Ellen DeGeneres Show, Josh admitted the pair first bonded over their similar sense of humour.
"She's, well, she's such a brilliant and funny person," he said. "Humour is such a huge thing for me, so the fact that we could talk about Monty Python and all sorts of weird other things, I was like, 'OK, yeah, we're on the same page.'"
Josh initially found fame as a singer and is also an incredibly talented songwriter. And during her appearance on Ellen, Kat revealed her beau used his writing skills and his humour to pen some hilarious songs about their daily chores.
"Obviously you know how talented and amazing (Josh) is," she said. "But what you may not know is that he's one of those people who can sit at a piano and play anything, anything off the top of his (head) … he's just, he's just a genius.
"Once I was steam cleaning the floor – because I like to steam clean. And he sat down at the piano and made up a song called Steam Cleaner Lady."
Neither Josh nor Kat have broached the split reports on their social media pages. WENN has contacted representatives for both stars for comment.
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