Full-back Byrne will move to Rodney Parade from French heavyweights Clermont Auvergne during the summer after agreeing a two-year contract.
Wing Brew, meanwhile, rejoins the Dragons on a three-year deal following two years spent in the French Top 14 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," former Ospreys star Byrne, 33, said.
And nine times-capped Brew, 27, 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 for me and my family."
The deals represent a significant double capture for the Dragons, a fact not lost on their rugby director Lyn Jones.
"I am absolutely delighted to sign someone of Lee's experience and calibre," Jones said.
"He has proved himself in Britain and France as a top-quality number 15.
"It's a significant signing for us, a player who is going to help the growth of our Gwent side while helping to develop Hallam Amos as a future Welsh 15.
"Aled has shown a desire to come back to his natural home of Newport Gwent Dragons, where he was extremely popular with the supporters in the past and proved to be an excellent try-scorer."