Reading missed out on promotion last season under Steve Coppell after a play-off defeat to Burnley and have turned to their former academy coach Rodgers as his replacement.
Rodgers, 36, spent nine years with the club before leaving for Chelsea in 2004 and admitted he left Watford to steer Reading back to the top flight.
He said: "I've had an association with Reading since I was 13 years of age and I've seen the growth over the last 20 years.
"It's a Premier League club now, without a doubt, and I'm very proud to be here.
"I wasn't crying to leave Watford but this is an opportunity to become the second manager in history to take Reading into the Premier League.
"Promotion will be talked about but my ambition is much more than that.
"This club has been managed exceptionally well over the last 20 years. It is run on very sound business principles and the aim is to be a sustainable club in the top flight."
Watford chairman Jimmy Russo was disappointed by Rodgers' decision to leave Vicarage Road on Thursday after just 192 days in charge but the Northern Irishman insisted he had nothing to defend.
Rodgers steered the Hornets away from relegation danger in his short stay and also managed to blood youngsters such as Ross Jenkins and Scott Loach.
He said: "There's always sadness when you leave.
"I was committed and happy but once the approach came in from Reading then I had some thinking to do and I wanted to speak to them.
"I absolutely didn't leave Watford in the lurch. We galvanised the club and changed the football philosophy there.
"When I left Reading five years ago my departing comment was that I would return as manager. Maybe that was a bit tongue in cheek but I had the ambition to do that and now I am here."
Chairman Sir John Madejski felt that Rodgers' previous time at the club meant he was the only man capable of replacing Coppell.
Coppell became the most successful manager in Reading history during his six-year stay but Madejski is confident Rodgers can match that success and win promotion.
He said: "I'm delighted he's come back after learning from the chosen one and at Watford where he proved himself.
"He knows the Reading way and we think he is the chosen one.
"We know him, he is not an unknown quantity. He has some great ideas for the club and he made it easy for us to bring him back here."
Rodgers expects to be joined by his backroom staff from Watford of Frank Lampard Snr and Dean Austin in the next few days ahead of pre-season training which begins on July 6.