The 29-year-old midfielder was greeted by dozens of Roma supporters as he arrived at the airport in the Italian capital, before the club posted images of the player having a medical.
Roma paid an initial fee of 26.65 million euros (30 million euros) for Nzonzi, who featured in five of France's seven games at the World Cup, including an appearance off the bench in the 4-2 win over Croatia in the final.
"I feel very happy to be here, and to be a new Roma player," Nzonzi told the club's official website.
"I really felt that the club wanted me to come. I will give my best on the pitch, and hopefully be a very good player for this team.
"I always want to improve - regardless of age, the most important thing is to give your best and work hard. I want to do that, to become a better player and help the team with my play and experience."
Nzonzi joined Sevilla from English club Stoke in 2015, and was part of the team that beat Liverpool 3-1 in the Europa League final in 2016.
"Steven is a footballer with a mix of physical and technical qualities that we think will really add to the players that we already have here," said Roma sporting director Monchi, who left a similar role at Sevilla for Italy last year.
"With his arrival, we have even more quality and competition in midfield."
Roma, who finished third in Serie A last season and reached the semi-finals of the Champions League, begin the new campaign away to Torino on Sunday.