The 24-year-old former Penrith junior will join the Belmore club on a two-year deal next year.
During his time with the Storm, Turner has collected two premierships and an NRL title in 2007.
“Steve has been very impressive both on and off the field,” Bulldogs head coach Kevin Moore told AAP.
“He is a quality player with great experience for a 24-year-old, he can play in a variety of key positions and we think he will be another great addition to our club.”
“I have been closely monitoring the Bulldogs this year and I think it will be the perfect environment to further my football career.” said Turner.
“The Bulldogs culture of a family club is something I like and there style of footy suits the way I like to play.”