The 17-year old defender made the switch from Dinamo Zagreb for a fee of £4.3million earlier this week, despite Spurs' best efforts to bring him to White Hart Lane.
Jedvaj has represented Croatia at Under-19 level and the highly-rated youngster says that Roma beat a number of teams to complete the deal.
"I had many clubs who were interested in me, it's useless saying names," he told Roma's official website.
"The most important thing is being here. This is a club with a big history, with big names on the pitch.
"I'm sure I have joined one of the top three Italian sides. Everything went quickly and I didn't follow the news that they were talking about my arrival here."
Tottenham were reported to have been close to Jedvaj's signature but he says that the Italian side came in with a better offer and he has signed a three-year deal.
"In the last weeks, there had been a strong interest from Tottenham, but Roma did a strong negotiation and now I'm happy to be in this group, " he added.
"My hope is to win titles, to repay the faith the club showed me and to show myself at the best of my potential to help Roma gett a European place.
"My main aim is to stay here, playing with Roma and staying for many years. I feel myself ready to play with the main team and not the youth one.
"Do I know about Marquinhos? Sure, he only started playing with Roma last year and now the whole of Europe knows him. He's the best example that age doesn't count."