De Rossi, who was appointed in January on a deal that ran until the end of the season, replaced Jose Mourinho and took over a side that was ninth in the league's standings.
Under the former Italy international, Roma have climbed to fifth in the standings following a seven-game unbeaten run in the league.
They have also reached the Europa League quarter-finals, in which they have a 1-0 advantage over opponents AC Milan heading into Thursday's second leg.
"After meeting yesterday afternoon with Daniele De Rossi, we are delighted to announce he will continue as head coach of AS Roma after this season and for the foreseeable future," club owners Dan and Ryan Friedkin said in a joint statement.
"In his short tenure as head coach, the positive impact that his leadership has brought to the entire club has told its own story.
"Daniele leads with respect and courage, while his strength and deep-rooted belief in the club are truly aligned with Roma's values, city and unparalleled fans."
The club did not provide any details on the length of De Rossi's contract.
Roma next host Milan in the Europa League later on Thursday, before taking on Bologna in a league clash on Monday.
