The deal appeared to be on the verge of collapse because of the striker's demands, but he is now set to sign a contract with the Giallorossi, reportedly for five years.
The forward is currently co-owned by Genoa and Siena, but both clubs have already agreed to sell the 21-year-old to the Giallorossi.
The transfer was held up by Destro's wage demands but, according to the man himself, a deal has now been brokered.
"The soap opera is over," Destro, who will apparently sign a five-year contract with Roma, told Sky Sport Italia. "I am very happy."
Roma boss Zdenek Zeman is just as enthused by the striker's belated arrival at Trigoria, adding: "I'm glad that he's coming. With him we have another solution in attack."
Destro, who was included in Italy's preliminary panel for Euro 2012, netted 12 times in 30 Serie A appearances for Siena last season.