Smalling impressed during his season on loan in the Italian capital last season, playing 37 times as Roma finished fifth in the league and reached the Europa League quarter-finals.
The 30-year-old joined United in 2010 from Fulham and went on to make 323 appearances for the club across all competitions, scoring 18 goals.
He won two Premier League titles with the Red Devils and tasted success in the FA Cup, EFL Cup and Europa League.
The 31-cap England international will hope to make his first appearance as a permanent Roma player when they host Benevento after the international break on 19 October.
United signed Alex Telles from Porto on Monday and are expected to confirm the arrival of Edinson Cavani on a free transfer, while Diego Perotti and Justin Kluivert both left Roma on loan to join Fenerbahce and RB Leipzig respectively.