The French teenager became Rodgers' first signing as Celtic manager on Tuesday almost six months after his agent was first approached by Parkhead scout David Moss.
The 19-year-old was in demand after netting 17 goals for Fulham last season and a January move to Tottenham broke down after advanced negotiations.
But the striker - who signed a four-year contract - believes Glasgow is the best destination for him to progress his career.
"I first heard of Celtic's interest in January," he said after being paraded at Celtic Park. " I have thought about it since January but I had a few other options. I took my time and looked at all the options and Celtic came up as the best choice.
"I had a few (offers) but I didn't have the same one I had with Celtic in terms of football. I think it's the best place for me to be."
While Dembele was firmly on Celtic's radar before Rodgers took over last month, the former Liverpool manager threw his weight behind the club's move to help it succeed.
"When you have a manager like Brendan who talks to you about the club and who convinces you to come, it's a massive thing," said Dembele, who spent four seasons in west London after leaving Paris St Germain's youth set-up.
"He told me about the club, about what he wanted to do with me in the future, and I was happy with that. Brendan is a very big manager and I can't wait to work with him."
Dembele was linked with the likes of Arsenal, Liverpool, Juventus and Stuttgart but his decision was swayed by the chance to feature in the Champions League.
"I signed for Celtic because it's a massive club in Europe," said Dembele, who cost Celtic a six-figure compensation fee. "I want to play in the Champions League and I think I can do this here.
"It would be special. As a young boy you always dream of playing in the Champions League. We have a chance to do that this season. It's up to us, we have to win the qualifiers.
"I want to score goals, I'm a striker. I want to score goals and win trophies because Celtic is a club that wins trophies.
"I came to Celtic to improve. I was in the Championship and I've come to the Scottish Premiership. I see my future here and hopefully I can score a lot of goals for the club and win many trophies."
The France youth international has been doing his homework since Celtic's interest emerged, research which included getting recommendations from Fulham strike partner Ross McCormack.
"Last season I watched a lot of Scottish football," he said. "I know the club well, and the unbelievable fans. It's one of the biggest clubs in Europe and I can't wait to start.
"As a young boy you always know about Celtic, because the club is massive in Europe so you have always heard of them.
"And last season I started to watch closely the Scottish league."
Dembele did not have detailed discussions with Rodgers over where he will fit into the Celtic team. Leigh Griffiths hit 40 goals last season in a lone central striker role, but Dembele is keen to build up a partnership with the Scotland international.
"We have to work hard together for the team," he said. "One individual is not bigger than the club so we have to work together to make the club better."