Mulumbu returns to Celtic after joining in January for a second spell at Rugby Park.

Daniel Bachmann, Aaron Tshibola, Conor McAleny, Mikael Ndjoli and Liam Miller also return to their parent clubs.

But Ndjoli and Miller are out of contract this summer.

It follows manager Steve Clarke's decision to leave Kilmarnock after guiding the club into the Europa League and achieving its record top-flight points total.