Bryant, 29, won his only Wales cap as a replacement in 2003, while Thomas, 21, has played for Wales at all age groups.
"Lee is young but has the potential to develop in to a top player," said Sale rugby director Philippe Saint-Andre.
"John will fit extremely well in to our side. He has the ability to break the defensive line with power and pace."
Evans has won 27 caps and was a key player in the winning run under Graham Henry in 1999.
But he has not played internationals in the last two years and has been mostly on the bench for the Blues this season.
Bryant has scored one try in 17 appearances for the Dragons this season.
He said he had no hesitation in leaving Rodney Parade to join the Guinness Premiership leaders.
"Once I knew Sale Sharks were interested in me, it was a very easy decision to make," said Bryant.
"I want to play rugby at the top level, and Sale Sharks are very much a club on the up both in the Premiership and in Europe.
"I will be very disappointed if I am not winning major honours with Sale during my time there."
Thomas has found opportunities limited at the Blues this season, and is likely to find himself in a similar position at Sale as he plays understudy to first-choice fly-half Charlie Hodgson.
But the versatile back believes a move to Edgeley Park will make him a better player.
He said: "It will be a wrench to leave Cardiff, but I am a young and very ambitious player.
"The opportunity to join Sale and to learn from the likes of Charlie Hodgson was too good an opportunity to turn down.
"I believe my game already offers something new to Sale, and am certain that under the coaching of Philippe St Andre and Kingsley Jones that my game will come on leaps and bounds."