The young forward has now sealed a permanent move after already spending last season on loan at the Stadio Olimpico side, where he scored 11 goals in 26 appearances
The 22-year-old joined the Giallorossi on a one-year loan deal worth £9.8m in the summer of 2012 and they have now opted to exercise their option to acquire 100 per cent of his economic rights for an additional £3.8m.
Destro initially struggled to live up to the high expectations following his move to Roma, but ended the 2012-13 campaign with 11 goals in 26 appearances in all competitions.
The attacker, who has already been capped at senior level for Italy, is a product of the Inter youth academy but never made it into the first team at the Nerazzurri.
He was part of the Azzurrini Under-21 team that made it to the final at this summer's European Championship, where they were beaten 4-2 by Spain.