The right-back signs a five-year contract with the Serie A side.
After rising through Feyenoord's youth system, the 22-year-old made over 100 appearances for the first-team. After playing a key role in the Rotterdam side's Eredivisie title win, he spoke of his excitement at making the switch to the Italian capital.
"Moving to Roma is a big step for me," he told the club's official website. "I come here with great desire and enthusiasm to play and realise my dreams.
"I know I still have room for improvement and I hope to do that here."
Roma sporting director Monchi said he is confident he can flourish in new coach Eusebio Di Francesco's team.
"Despite his young age, Karsdorp has already shown his qualities," he said. "We are delighted to be able to count on his performances and we are confident that he will fit Eusebio Di Francesco's style."
Karsdorp joined Feyenoord in 2004 and made his first appearance for the first-team 10 years later.