Mujati, 32, signed for Ospreys from English Premiership side Sale Sharks in February as cover for Dmitri Arhip and Ma'afu Fia, who were out with injury.
The former Springbok has started seven of the last eight games for the region.
"I've settled in really well here and I'm thrilled to be staying with the Ospreys longer-term," Mujati said.
He continued: "My family is here with me and everybody has made us really welcome. It's a good environment to be in.
"While I'm pleased to be with the Ospreys next season, we have some really important business ahead of us on the field and that has to be the focus for everybody over the next few weeks."
Mujati has played in South Africa's Super Rugby with Lions and Stormers, in Top 14 in France with Racing Metro, and in England with Northampton Saints and Sale.
"It's always difficult for a player moving to a new team in-season and having to learn on the go but Brian has adapted to what we want really well, like the professional that he is," Ospreys head coach Steve Tandy said.
"With the continued absence of Dmitri and Ma'afu, Brian has had a big role to play. With a good pre-season under his belt, I think we'll truly see the best of him."
Ospreys prop Brian Mujati will remain with the region for 2017-18 after initially signing a deal until the end of this season.