Destro joined the Rome-based outfit from Siena this summer before being reportedly courted by Genoa and Juventus as well.
The 21-year-old is looking forward to his adventure with the Lupi and is confident that they can challenge for top honours.
"We will certainly have a great season," Destro told Roma Channel. "If we are in good shape in February and March, then why not challenge for something?
"I always said I am ready to play wherever the coach wants me to. I want to do really well and score more than I did last season. After all, it's easier to score goals with (Zdenek) Zeman.
"The Giallorossi have a wonderful group of players and I was given a warm welcome. There are many youngsters here, but it's the right mix with experienced elements."
Roma finished seventh in Serie A last season under Luis Enrique, who was replaced by Zema this summer.