Byrne will move to Rodney Parade from French side Clermont Auvergne during the summer after the full-back agreed a two-year contract. Brew, meanwhile, rejoins the Dragons on a three-year deal following two years spent on the wing with Biarritz.
Byrne has won 46 caps and toured with the 2009 British and Irish Lions in South Africa. He is currently sidelined with a dislocated shoulder.
"I am excited to be returning to Wales to play again, I hope to bring my experiences from France back to the Dragons," said the former Ospreys player.
And nine times-capped Brew, added: "I have really enjoyed my time in France and would like to think I've learned a lot during my time in Biarritz and that I've become a better player because of it.
"I have no regrets at all about my time in French rugby. It has been a fantastic experience, but I feel it's the right time to come home."