“This is an opportunity that came to me that I was very interested in, and I was very eager to come,” the 29-year-old defender said during his official presentation in Rome.
“To have a chance at a big club, if it prolongs and the club is happy and I am happy, then I can definitely see a longer term future in Italy.
“Serie A has always been a goal of mine.
“In England we don’t have many players who do go abroad, but I’ve always had a desire deep down to experience this and to have the opportunity to go to a big club with big aspirations.”
Smalling, who has 31 caps for England, made 323 appearances for United during nine years at Old Trafford, winning the Premier League twice.
But he has fallen out of favour since the signing of Harry Maguire for £80 million (90 million euros, $97 million) from Leicester City.
His move cost the Italian team three million euros as they look to return to Champions League football after finishing sixth last season.
“I spoke to (Roma coach Paulo) Fonseca before I came to the club and he told me his goals, what he wanted from me. It was something that we totally agreed on,” he said.
“He wants a defender that is aggressive and can cope with the runs in behind and, yes, I think it is a perfect fit (for me).”
Roma have been short at the back since Greece international Kostas Manolas left for Napoli for a reported fee of 36 million euros, and are 15th in Serie A after being held in their opening two fixtures by Genoa and city rivals Lazio.
“I am not a young player who has to prove himself –- but I like new challenges,” Smalling continued.
“At Manchester we had high expectations, but here in Rome there are high expectations too,” added the defender who says the club are “one of the favourites” to win the Europa League.
Smalling added he had no doubts moving to Rome despite his charity work in Britain and vegan lifestyle.
“When I spoke to the club they knew the interest I had in my charity work, and also my vegan lifestyle. The club has put me at ease about that straight away,” he said.
“I’ve been speaking about the chef and the nutritionist and we are looking at different menus and things. I did not have any worries about that, from day one.”
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