The 20-year-old was part of the Benfica side that won a domestic treble and reached the Europa League final last season, and he is looking forward to challenging on all fronts once again having seen Liverpool narrowly miss out on the league title in May.
"The Premier League is the strongest league in the world, and so I am very happy to be here. 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," Markovic told the club's official website.
"I watched every [Liverpool] game [last season] and they played absolutely superb. It is a shame they did not win the 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%."