Defender Winston Reid has signed a new long-term contract with West Ham which commits him until the summer of 2021.
Blackburn have signed defender Doneil Henry on a month's loan from West Ham.
Olofinjana has found playing time hard to come by since returning from a serious knee injury that put him on the sidelines for nearly a year.
He has only made 39 appearances for the Tigers since signing for a fee of £3m in the summer of 2009 but did have a successful loan spell with Cardiff, where he scored six goals in 39 games.
The Nigerian midfielder is in line to make his Owls debut against local rivals Barnsley at Hillsborough on Saturday.