The staff, announced Tuesday, will also include bullpen coach Rick Adair, third base coach John Russell and first base coach Wayne Kirby.
Randolph spent the past two seasons as bench coach of the Milwaukee Brewers. Before that, he managed the New York Mets from 2005-08.
Connor spent the past eight years in the Texas Rangers organization. He served as pitching coach for Showalter in his two other managerial stints with the Arizona Diamondbacks and New York Yankees. He takes over for Rick Kranitz.