Kush was the first of the Chiefs' two sixth-round picks out of California (Pa.), while Catapano was their seventh-round selection out of Princeton.
The Chiefs announced the signings Friday. No terms were disclosed.
The Chiefs also signed 13 college free agents, including former Tennessee quarterback Tyler Bray, Florida wide receiver Frankie Hammond Jr. and UW-Milwaukee hoops player Demetrius Harris.
The Chiefs were scheduled to work out their rookies Friday, Saturday and Sunday before the rest of the team joins them for the start of organized team activities on Tuesday.