Wing Prydie, who became the youngest player capped by Wales when he faced Italy in the 2010 Six Nations aged 18 years and 25 days, joins from the Ospreys after falling down the pecking order and being loaned out to Wasps.
Full-back Evans, 23, who featured for Wales on the 2009 tour of North America, moves from the Scarlets and the pair will fill the gap left by the departures of Aled Brew and Martyn Thomas from Rodney Parade.
"I'm really looking forward to the new challenge that signing with the Dragons presents." said 20-year-old Prydie.
"I've worked with (Dragons coach) Darren (Edwards) before and felt I learned a lot from the time I spent with him. I really enjoyed the experience so I am looking forward to getting involved in a new environment down at the Dragons next season.
"This season has felt a bit stop-start, particularly at the start of the season, so it will be great to have a fresh start and a bit of consistency.
"There is a lot of potential at the Dragons and hopefully we can be very competitive next season."