Markovic, a Serbian international, played for Benfica last season, which reached the Europa League final. The 20-year-old scored five goals in five games in the Portuguese Liga.
"I hope that I will fulfil (sic) 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."
Manager Brendan Rodgers' club has also signed Rickie Lambert, Adam Lallana and Emre Can this summer.
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- Sarah Barshop