The couple were photographed holding hands and sharing a joke at an event celebrating British Airways' Inaugural A380 service from London to Los Angeles on Wednesday (25 September).
28-year-old Kelly looked beautiful in a monochrome mini-dress with statement necklace, while Matthew smartened his grey jeans with a navy blazer.
Kelly and Matthew announced their engagement in July, although it's believed Matthew popped the question before that while they were on holiday in the Caribbean.
The couple met at mutual friend Kate Moss' wedding back in 2011. Matthew is the brother of Kate's husband Jamie Hince's bandmate Alison Mosshart.
Los Angeles-based Kelly recently gushed about vegan chef Matthew in an interview with Cosmopolitan magazine, saying: "I'm so lucky to have somebody as special as Matthew. I tend not to talk about relationships, because everything else is so out there and the only thing that is mine is my fiancé.
"The only thing I'll say is that you will never learn what love is on any level until you let someone love you the way you deserve to be loved."
Kelly and Matthew have so far kept tight-lipped on wedding plans, but Sharon revealed on her US show The Talk that Kelly is hoping to wed next summer at the Osbourne family home in England.
Watch Sharon announcing Kelly's engagement on US TV: