The fight will take place on the undercard for the Carl Froch v Mikkel Kessler super-middleweight double world championship clash at the O2 Arena.
The winner will meet either champion Chad Dawson or first challenger Adonis Stevenson – with that duo due fight in June or possibly even on the same night as Bellew and Chilemba.
Bellew called foul after his first fight with the Malawian-born Chilemba was ruled a draw in front of his hometown fans in Liverpool nine days ago.
The judges scored that contest 116-112 Chilemba, 116-115 Bellew and 114-114.
"I thought I won nine out of the 12 rounds and even Chilemba's trainer, Buddy McGirt, one of the most respected men in boxing, told me he thought I won," said Bellew after that contest.
"I've got a lot of time for Chilemba. He's a good fighter and a tough man but I won the fight."