Odubajo has signed a three-year deal at Griffin Park, and Bees boss Mark Warburton believes that the 20-year-old will prove to be an "exciting addition" to his first-team squad.
The 51-year-old told the club's official website: "We have been very impressed with his quality and his consistency.
"Moses is a young player with a lot of development potential. I am sure that he will prove to be an exciting addition."
Odubajo netted 12 goals in 57 appearances for Orient during the last campaign.