Quinn, who has long been linked with a move across the city, and Bromby were released at the end of last season by Chris Turner.
The signing of Bromby comes of something as a surprise although speculation was mounting in the last few days that he could join The Blades.
Warnock has been tracking Quinn's signature for a few years now and is overjoyed to finally get his man.
The deals for Quinn and Bromby will add to Warnock's other confirmed signings: Jon Harley and Barry Hayles.