The 33-year-old former Wolves and Stoke midfielder, released by Hull at the end of last season, has been training with Wednesday and signed a month-by-month deal in time to make his debut in the 1-1 draw at local rivals Barnsley at the weekend.
The Owls have drawn eight and lost five of their first 12 matches and slipped to the bottom of the Championship table courtesy of Yeovil's win over Nottingham Forest.
"We have a good group of players here and it's frustrating that we haven't got that win," Olofinjana said after his debut on Saturday.
"In ordinary circumstances, a point away in a derby game is a good point, but we are disappointed.
"Now we move on, we are a difficult side to beat, but we have to turn these draws into wins. We have the players here who can do that and I'm confident it will be done."
The Nigerian added: "I've waited patiently, trained hard and bided my time.
"I was offered a contract here and I couldn't wait to sign it. There have been other options available to me but I wanted this to be my club.
"I enjoyed my time here last season, the manager told me to keep working hard and my chance could come.
"It did and I'm happy to be back. I could see the potential here last season and was very keen to come back and be a part of it again and work under the manager."