The undisclosed fee was reported by British media to be £20m for a "long-term deal"
The 20-year-old is the fourth new arrival at Anfield this pre-season following Southampton and England duo Rickie Lambert and Adam Lallana, as well as Emre Can, while controversial striker Luis Suarez has left to join Barcelona in a £75m move.
Markovic made his name at Partizan Belgrade and won successive Serbian titles with them before leaving last year to join Benfica, where he helped the Lisbon side complete a Portuguese treble during the 2013/14 season and reach the UEFA Europa League final, where they lost to Spain's Sevilla.
"I am very happy that I have joined such a great club," Markovic told Liverpool's website. "I hope that I will fulfil the expectations of the supporters, coaches, players and all connected to the club."
Liverpool will be looking to go one better than last season after finishing runners-up in the Premier League to champions Manchester City, and Markovic is confident of adding England to the list of countries where he has won silverware.
"The Premier League is the strongest league in the world, and so I am very happy to be here," he said.
"And I have already played in the Champions League with Benfica. It is superb that Liverpool are in it and I hope we will go far next season. I watched every game (of Liverpool's last season, from portugal) and they played absolutely superb.
"It is a shame they did not win the (Premier League) title -- but I hope we will win it this season. 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 (Markovic) 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."