The 22-year-old Clarke will cover for the expected World Cup call-ups of Lawrence Dallaglio and Joe Worsley to the England squad during October and November.
The 25-year-old Richards adds to their scrum-half contingent after the departure of England 'A' player Martyn Wood to Bath, and will be battling with Welsh star Rob Howley for a starting place.
Wasps coach Warren Gatland said of his two new boys: "I'm delighted at Peter's and Ian's signings as I feel they will contribute a great deal to the club over the next season.
"With Martyn Wood leaving for Bath, we needed a good back-up to Rob Howley and I feel Peter will offer this.
"Clarke is still young, but he is a big strong forward who can play at six or eight. I'm assuming we will lose a few players to Clive Woodward's World Cup squad and so the new signings will offer decent back-up."
Wasps have already been active in the transfer market, with Bath wing Tom Voyce, Cardiff prop Tim Payne and Connacht flanker Johnny O'Connor having put pen to paper in recent months.
By Mark Smith