Robinson, left, has 13 international caps, while Davis is leaving Exeter
Wasps have signed fly-halves Nicky Robinson from Gloucester and Exeter's Ryan Davis, both on two-year contracts.
The two stand-offs will move to Adams Park to replace Dave Walder, who has confirmed he will leave the club to play overseas next season.
Wales international Robinson, 29, spent nine seasons with Cardiff Blues before moving to Kingsholm in 2009.
Davis, who is 25, joins Wasps after just one season with the Chiefs and six years at Bath.
Robinson told BBC Radio Gloucester: "I would have like to have extended my time here but that wasn't an option.
"Obviously I'm really pleased to be joining a club like Wasps who have some big ambitions.
"I'm enjoying my rugby here at the moment though and intend to do so until my contract is up."
Wasps chief executive Chris Thomas said: "We are really pleased to be able to bring in two experienced Premiership players in such a key position.
"With Dave Walder leaving, it was vital that we brought in talented replacements and we think these two players will fit in very well at Wasps as we look to strengthen our squad for next season."
I am now eager for a new challenge both on and off the field
Dave Walder on leaving Wasps
On Walder's departure Thomas said: "Having been with us since 2006, I know I speak for everyone when I say that Dave has left a real mark on the club.
"He has decided to prolong his career by playing abroad, something he has always wanted to do, and we fully support that decision."
Walder added: "I have really enjoyed the five seasons spent with London Wasps and would like to thank the squad, backroom staff and especially the fans for their support over that time.
"I am now eager for a new challenge both on and off the field and negotiations surrounding my next move are extremely positive and I am really excited about the future."