Odubajo has been an important player for Orient this season, chipping in with three goals in his 38 appearances for the club.
The 19-year-old's contract was due to expire at the end of the season and O's manager Russell Slade was keen to see the youngster put pen to paper.
He told the club's official website: "We're really pleased with Moses signing. He has made great progress this season and continues to improve enormously all the time. There is definitely more to come from him, and there is no doubt in my mind that one day he will play at a higher level.
"It's a signing that I'm sure will prove to be a massive asset for us not only for now but looking forwards as we continue to build a team for the future.
"There was a lot of interest in him as you can imagine as he is such a talented lad so it's all the better that he has signed and got things sorted. We really are delighted."
- Sports & Recreation
- Russell Slade