Meanwhile, striker Omar Bogle has left the club by mutual consent. He has linked up with League Two side Hartlepool.
Odubeko, 19, returned to London earlier this month following a spell with the Terriers where he played six times from the bench.
Four were in September and only two for more than 15 minutes. His final appearance came as a 55th-minute substitute at Barnsley in early December.
On the decision to let him head back to West Ham, Huddersfield head coach Carlos Corberan - speaking earlier this month - said: Corberan added: "First of all, I wish him all the best. He's a good lad and worked hard for me, but the loan was to help him develop because he needed something more than U23 football. But sometimes the first part of a loan is the most complicated step.
"I saw a more mature and capable player in the second part of the loan, but we couldn't guarantee him the minutes that he needs. I think he's more ready for senior football and now need minutes to show those skills in a real situation.
"I'm convinced he's a player with a lot of potential and a special talent for finishing and I wish him the best."
Odubeko was a prolific scorer for the Hammers’ under-23s team in Premier League 2, and was involved in 18 matchday squads for the first-team last season - making his debut in the Emirates FA Cup victory at Stockport County.
His arrival at Rovers follows this week's capture of experienced midfielder Adam Clayton.