Kompany has missed City's last four matches after serving a suspension for his controversial sending off in the FA Cup third-round loss to Manchester United. Without him, City had to dig deep to claim narrow Barclays Premier League wins over Wigan and Tottenham while they were beaten by Liverpool over two legs in the Carling Cup semi-finals.
The Belgian defender had been in commanding form before his ban and Richards believes his return, for the league leaders' trip to Everton, is timely. Richards said: "He has been an unbelievable miss. He is our captain and he and Joleon (Lescott) have been our best central defensive partnership this season."
He added: "He has played well in the big games and is a leader so it will be amazing to have him back and we can't wait to play with him again.
"He has still been coming in the changing room before games and saying how he feels we can improve, and what he would do if he was on the pitch, so he has still been an influence.
"But it's not nice for anyone. All the players and staff wanted him to play and he was kicking himself because it was another harsh decision to give him the ban.
"I am sure when he comes back he will give 110% and help us back to winning ways."
Kompany's return will probably see Richards revert to sharing right-back duties with Pablo Zabaleta after featuring as one of three centre-backs in the second leg against Liverpool last Wednesday.
Richards, who also wore the captain's armband at Anfield, said: "I have played right-back for the last couple of seasons and am enjoying it but if the manager needs me to play centre-back if there's an injury or something I will have to do so.
"Vinny is coming back now and he and Joleon have it pretty much sorted out back there, and there will be more competition when Kolo (Toure) comes back."