Bishop, who recorded 11 sacks last season for Calgary, signed a two-year deal, ESPN NFL Insider Adam Schefter reported. Bishop (6-foot-3, 255 pounds) was undrafted out of Western Michigan in 2013. He was released last season by the Detroit Lions.
Seven teams showed interest in Bishop, who projects as an outside linebacker in the Jets' scheme.
The Jets signed Brindza to create flexibility at kicker. Randy Bullock, who replaced the injured Nick Folk at midseason, is a pending free agent. Folk is under contract, but he has the eighth-highest cap figure for kickers ($3.3 million) and could be released.
Brindza made six of 12 field goal attempts last season for the Bucs.