The 22-year-old left-back's exit from the Stadio Olimpico follows Roma's capture of Ashley Cole on Monday.
Dodo initially joins Inter on a two-year loan at a cost of €1.2 million, but the deal includes an obligatory buy-out clause of €7.8m, to come into effect when he plays his first official game.
In a statement welcoming Dodo to the club, Inter said: "The player has signed a contract until June 2019."
Roma had earlier confirmed Dodo's departure in a statement of their own, which read: "AS Roma SpA announces that it has signed with FC Internazionale Milano SpA for the temporary transfer and two-year rights to the player JR Pires Ribeiro [Dodo], against a payment of € 1.2 million.
"The agreement, valid for the seasons 2014/2015 and 2015/2016, provides for the compulsory acquisition outright, conditional on the player's first presence in official matches of the first team, with a value of € 7.8 million."
Dodo, who joined Roma from Corinthians in 2012, featured in 19 Serie A matches for Rudi Garcia's men last term.
