The 20-year-old winger completed his move to the Reds this afternoon having impressed during the Portuguese club's treble-winning 2013-14 campaign.
Rodgers believes that Liverpool have done well to get the Serbian at such a young age and is excited at the prospect of him coming into the team this season.
"This is an exciting signing for us and one that improves our squad, in terms of attacking options, for the coming season. He was hugely impressive for Benfica last season and has proved he has the ability to produce the goods in European competition as well, which will be important for us," Rodgers told the club's official website.
"Lazar is flexible to play a number of positions, but I like the way he attacks games and is always positive and looking to make something happen. He will fit in with the way we play at Liverpool.
"Getting him at such a young age is also very pleasing for us, because we will be able to work with him to develop his talent within our group and improve him even further. He is the sort of character who is hungry to get better and progress; this is what we look for in players."