The 20-year-old striker made his first-team debut for Wanderers away to Charlton in March and has gone on to make five further appearances for the club, netting twice in Bolton's 3-1 win over Shrewsbury in the Capital One Cup in August.
"I'm delighted to have signed a new deal," Odelusi told the club's official website.
"It's now time for me to get my head down and continue to work hard. I want to be pushing for more first team appearances.
"Hopefully I'll get my chance. I want to show people how much it means for me to be here.
"Since the manager and his staff came in I feel they have helped develop my game both on and off the pitch. I want that to continue."