The 22-year-old has made nearly 80 appearances for the Welsh side since his debut in 2010.
Evans is expected to sign for Bath before the 2015-16 campaign.
"We are sad to see Jonathan leave us but we wish him all the best," director of rugby Lyn Jones told Newport's official website. "He still has a lot of game time left with us at the Dragons and I hope that he intends on leaving the club on a high note. We hope to see him back at the Dragons in the future."
Newport are back in action tomorrow when they host Exeter Chiefs in the LV= Cup.