The 20-year-old, who made his first-team debut in March, has made five appearances for the Championship outfit.
"I'm delighted to have signed a new deal. 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," Odelusi told the club's official website.
"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."
Odelusi scored twice in Bolton's League Cup win over Shrewsbury Town in August.