The 27-year-old has been a regular for Wales since 2009, winning 42 caps for the Six Nations champions.
Director of rugby Dai Young told Wasps' official website: "We have a pool of very good locks here and bringing someone like Bradley in will only broaden that group, offering us huge experience and quality.
"I know Bradley quite well and he is a great guy to have in your squad. He is a proven leader which has been recognised with him captaining his country, and, as we continue to strengthen our side, I think he will be an excellent player for us."
Davies has spent the last nine years at Cardiff after signing his first professional deal as a teenager.