The 23-year-old will wear the number nine shirt at Roma and becomes the club’s fourth signing of the summer.
“You can sense when a club really wants you – and Roma made their interest clear immediately,” Abraham said.
“Roma is a club that deserves to be fighting for titles and trophies. I’ve had the experience of winning major trophies and I want to be in those competitions again – so I want to help this team to achieve that and get to the level where Roma should be.
“It’s a massive honour to be the No. 9 at this club and I just can’t wait to get started and to help the team.”
Abraham will have the task of replacing Edin Dzeko’s goal output after the former Manchester City forward departed Rome for Inter Milan on Saturday.
Roma’s General Manager Tiago Pinto said: “Despite still being very young, with a huge amount of potential to keep improving, Tammy has already played more than 200 games in his career and scored over 100 goals – and won a number of major trophies too.
“Choosing to leave the Premier League, and the club he grew up at, demonstrates very clearly just how much he believes in this opportunity to develop his own game and show what he can do at Roma.
“Bringing in players that have such a hunger and desire to play for our club is hugely important in helping to build the identity and sense of belonging that is a fundamental part of our overall vision for this team.”
Roma have also signed Rui Patricio, Eldor Shomurodov and Matias Vina this transfer window. Roma’s opening Serie A game of the season is at home against Fiorentina on Sunday.