Evans, a 23-year-old full-back has agreed to make the switch from the Scarlets, while 20-year-old winger Prydie joins from the Ospreys via Wasps.
The duo will replace Aled Brew and Martyn Thomas, who left Rodney Parade at the end of the season.
Evans has been capped twice by Wales, although his last appearance cap in 2009, while Prydie has made four appearances for the national team.
Prydie was the youngest player to represent Wales when he faced Italy in 2010, while he became his country's youngest try-scorer when he scored against South Africa.
Evans said: "I'm really looking forward to it. It's exciting to be joining a squad with the amount of young talent that the Dragons has at the moment.
"I'm eager to press for some more game time and hopefully help push for a successful season here at the Dragons."
Prydie, who is part of the Wales Under-20s side at the IRB Junior World Championships, ended last season on loan at Wasps after he struggled for game time at the Ospreys.
And he is relishing the chance to kick-start his career at Rodney Parade.
"I'm really looking forward to the new challenge that signing with the Dragons presents," said Prydie. "I've worked with Darren Edwards before and felt I learned a lot from the time I spent with him. I really enjoyed the experience so am looking forward to getting involved in a new environment down at the Dragons next season."
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