The 20-year-old Serbia international has joined the Premier League club on a long-term deal for a reported fee of £20m.
Markovic leaves Benfica following a one-season spell with the Portuguese outfit, where he scored six goals in 39 games.
"I am very happy that I have joined such a great club," he told Liverpool'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."
Markovic has scored two goals in 12 appearances for the Serbian national team.