The 20-year-old forward, who can play as a winger or as a conventional striker, has signed what the Reds are describing as a "long-term'" deal.
Sky Sports understands the transfer fee is in the region of £20million and Markovic is excited about the switch.
"I am very happy that I have joined such a great club," he told his new club's official website.
"I hope that I will fulfil the expectations of the supporters, coaches, players, and all connected to the club.
"I have seen what the players are like, I have seen what the supporters are like, and I cannot wait to start playing here.
"I went to Partizan and won the title, I went to Benfica and won the title. Now I have joined Liverpool and want to win the title, 100 per cent."
Liverpool manager Brendan Rodgers added: "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.
"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."
A product of Partizan Belgrade’s youth system, Markovic is a full international with 12 caps and two goals to his name.
The youngster helped Benfica to a domestic treble last season and made 13 appearances in Europe as the club overcame an early exit from the UEFA Champions League to reach the Europa League final.
Markovic becomes Liverpool’s fourth signing since the conclusion of the 2013/14 campaign following Rickie Lambert, Adam Lallana and Emre Can.
But the Reds have parted company with last season’s top scorer Luis Suarez, who is poised to join Spanish side Barcelona imminently.
Coutinho I don't think was given the chance to shine at Inter, he was always quality so there was no lucking out involved other than getting him so cheaply.- lfcfan80