The 20-year-old Serbian has signed a long-term contract at Anfield following a £20 million move from Benfica.
He is likely to provide competition in the final third of the field amongst players like Raheem Sterling, Philippe Coutinho, youngster Jordon Ibe and fellow new signing Adam Lallana.
He told the official Liverpool 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."
He becomes the fourth signing of the summer for the Reds as they continue to strengthen their squad ahead of the new season, which includes a return to Champions League football for the first time since 2009.
Markovic is unlikely to be the last player to sign for Liverpool during this transfer window as the Reds are said to be targeting more defenders and forwards.