McKenzie will fight in the -60kg category along with Graham Trinder while Conway joins Megan Fletcher in competing in the -70kg at the Europeans, which run from April 25-27.
Chris Sherrington, who joined McKenzie and Conway at London 2012, takes to the mat in the +100kg alongside Matthew Clempner while Ben Fletcher is the sole Brit at -100kg.
Nekoda Davies makes her European debut at -57kg with Connie Ramsay the other Brit at that weight with Natalie Powell fighting at -78kg in the Hungarian capital.
Sisters Kimberley and Louise Renicks will fight at -48kg and -52kg respectively and Tom Davis and Andrew Burns -81kg and -90kg with Patrick Dawson and Jan Gosiewski the British pairing at -73kg.
- Sports & Recreation