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The 27-year-old would play for the Pretoria side in 2012 and 2013, the Bulls said in a statement on Friday.
Steyn was born in Pretoria, schooled there and attended the University of Pretoria, where he played Super Bowl rugby. He represented the Blue Bulls amateur side before embarking on a professional rugby career at the Pumas in 2008.
"It has been a dream of mine all my life [to sign with the Bulls]," Steyn said.
"Make no mistake, I loved my time at the Pumas and will always be very appreciative to them for the way my career could develop under coach Jimmy Stonehouse, but this is where I have always wanted to be."
Frans Ludeke, the Bulls' Super Rugby coach, said he was impressed by Steyn's performances in recent seasons.
"Dawie will add depth to our front row and we have all seen the importance of having that," Ludeke said.
"He has all the attributes associated with Bulls front rowers and should add real value to our effort. I would also like to thank the Pumas for their professionalism in the way they handled the release of Steyn to us."
