Alex Gidman left the club last month after four years in charge and the Pears have looked close to home for his replacement.
Richardson, who took 254 first-class wickets for Worcestershire as a player, worked as Gidman's deputy and Kadeer was already involved as second-team coach.
Richardson said: "I've been involved in the club for a long time now and know its rich history. It's a proud moment for me to take on this role at Worcestershire.
"Kadeer and I always work hard to improve and develop players and we look forward to working more closely with our professional squad and the famous production line of talent from our academy.
"All of our efforts will be on helping these players fulfil their potential, both individually and, most importantly, as a team.
"I feel that we've already got a good relationship with our members and supporters, and we'll be looking to build on that and look forward to sharing lots of memorable moments with them."