The Ireland-born 19-year-old spent the first half of this season on loan in the Championship with Huddersfield Town but only managed six appearances - all of which came off the bench.
Odubeko moved to England from Ireland in 2016 and he spent time in the academies of Manchester City and Manchester United before joining West Ham in 2017 on a three-year deal.
His scoring record at age group level was excellent, with 11 goals in nine appearances for the Hammers’ U18s and 13 goals in 15 games for the U23s.
Odubeko made his senior debut for West Ham in last season’s FA Cup, coming off the bench in the third round against Stockport County before a lengthy run-out in the fifth round against Manchester United. He was not in the squad for the fourth round tie against Rovers.
He also made 18 appearances in matchday squads for the Hammers in the Premier League last term.
Odubeko represented Republic of Ireland at age group level but also qualifies internationally for England and Nigeria. He has previously rejected call-ups for Ireland’s U21 group.