Richards, who also played for Bradford and Southampton, was forced to retire from the game in March 2005 after suffering from dizzy spells and headaches while at White Hart Lane.
A statement on the Wolves website read: "Everyone at Wolves was saddened to hear of the death of Dean Richards, who passed away this morning at the age of 36 after a long-term battle with serious illness.
"Wolves would like to take this opportunity to send their condolences to the former Molineux defender's family and friends."
The Black Country club announced they were planning a tribute to Richards ahead of next Sunday's game with Spurs at Molineux.
Richards home town club Bradford, said on www.bradfordcity.co.uk: "The club are truly devastated to hear of the death of former Bradford City fans' favourite Dean Richards."
Richards was forced to give up the game in March 2005 after suffering dizzy spells and headaches which were reportedly initially diagnosed as an inner ear infection.
A statement on the Tottenham website, read: "Everyone at Tottenham Hotspur was saddened to hear of the death of our former player Dean Richards, who passed away this morning at the age of 36 after a long-term battle with serious illness."
It continued: "There will be a tribute paid to the defender ahead of our fixture next Sunday at Molineux against his former club Wolves.
"We extend our sincere condolences to the family of Dean Richards at this very sad time."