Evans – who is equally comfortable playing at full back and fly half – is one of the brightest young stars in the Welsh game.
The 24-year-old – currently in Switzerland as part of the Wales preliminary squad preparing for Rugby World Cup – will make the move to Rodney Parade this summer.
Evans joins Dan Lydiate, Dane Blacker and Corey Baldwin as new recruits for the Men of Gwent ahead of the 2023/24 campaign.
Flanagan said: “We’re delighted that Cai is joining us and his ability to play in more than one position will be a real asset to our squad.
“Cai is a talented young man who continues to improve every season, underlined by his recent call-up into the international set-up with Wales.
“I’ve worked with Cai before, during our time together with Wales Under-20s in France, so know just how dedicated and professional he is. He’ll be determined to take this opportunity with Dragons.”
Evans made his Ospreys debut in 2017 and has gone on to make 34 appearances, scoring 35 points.
The Penarth-born back previously impressed for Wales Under-20s between 2018 and 2020, memorably kicking the winning penalty in a historic triumph over the Junior All Blacks.
Evans said: “I’m delighted to be joining the Dragons and immersing myself in a new environment.
“I’ve got a strong existing relationship with Dai, having been coached by him through age-grade rugby, and I’m determined to be a strong addition to an exciting group of young and ambitious players.”