The midfielder rejoins manager Steve Clarke, whom he worked with at West Brom, at Rugby Park following a two-week trial.
Mulumbu, an uncompromising central midfielder, has been available on a free since leaving Norwich at the end of last season following two years with the club.
However, it is with West Brom where he made his name, making over 200 appearances in a six-year spell with the club until his move to the Canaries in 2015.
Mulumbu, who scored in the 5-5 draw between West Brom and Manchester United in Sir Alex Ferguson’s final match as United boss, said the prospect of working with Clarke had been a big factor in his decision to join Killie.
He said on the club website: “Obviously I didn’t come to Kilmarnock just like that. I spoke with Steve Clarke and he told me everything about the club and that was a big impact that he came here.
“I worked with him for a year and I know he’s an honest manager. I know the way he trains and the way he wants to play so it suits me and was a big affect for me coming here.
“I’m looking forward to showing the real Mulumbu. I was with Norwich for two years and it didn’t work like I wanted, so I have something to prove.”