The England international midfielder signed a long-term deal with the Reds on Tuesday for a reported fee of £25m.
"We are delighted to have secured the services of one of the Premier League's top talents in signing Adam Lallana," Rodgers told the club's official website.
"What is apparent about Adam is that his character is on a par with his talent. He is an exceptional young man and someone who has a love for the game - and, most importantly, a desire to progress and improve.
"Adam is motivated by being the best he can be and being part of something special. We believe he fits right in with what we are trying to do at Liverpool."
The Merseysiders get their Premier League campaign underway at home to Lallana's former club Southampton on August 16.