It is understood that Richardson will not have a hands-on role at the club, but will be involved in developing the training facilities in addition to seeking a move to a new ground.
"I am excited to have become involved with London Wasps, a club I believe has a fantastic opportunity to move forward on and off the pitch," Richardson told the club's official website.
"I see my involvement as a big responsibility and this is a long-term challenge which I want to meet head-on. The club has been through some tough times but I am confident that, with the right management and commercial focus, new investment can really reinvigorate everything about London Wasps.
"Financial stability is our immediate focus and our aim is to become a self-sustainable business within a number of years."
Wasps currently sit seventh in the table.