"It was quite a surprise to a lot of us, but there was initial excitement from everyone," said Smalling.
"I knew the media would build up something about our relationship in the past. But from a personal point of view, it is a good thing because I have played under him.
"We have won trophies together. He made me captain in one of those finals - the 2017 EFL Cup final - as well, so having the chance to play under someone who you know is good, has been so successful and is so determined to win trophies at all costs is a positive.
"I know how big a deal it would be to bring a trophy of some sort to the club.
"Jose's history shows the club has picked the perfect man to do that."
Smalling also commented on thier disagreement at United when the centre-back insisted his was injured whiles the former FC Porto manager struggled to believe.
"Ultimately, if the manager wasn't speaking about you and didn't want you to play and push, that is when you need to worry because he has stopped caring about you, he doesn't want you involved and he doesn't want you to play.
"He is a born winner. He likes to push everyone to the limits. That is what he has done throughout his career and it has reaped results."
Smalling having talked of how surprised he was after the announcement of Jose as the new manager for Roma also stressed he was aware the media will by all means comment on their past relationship at Manchester United but is optimistic the club will be a competitive side with the arrival of a winning manager in the shape of Mourinho.
"For large parts of the last two seasons, we were very consistent and weren't far off," he added.
"Now it is about having the mentality of making sure when we do go through those tough times, and maybe we aren't quite creating enough chances, we need to stick together.
"Now it is about finding that consistency. Hopefully with Jose and his staff we do that because it is such a great club.
"There is a good feeling around the club. All the foundations are there. It is just a case of bringing it all together now."
Mourinho and Roma will face Fiorentina in their 2021/22 Serie A opener on 22 August.
