Benfica confirmed they had sold their 50 per cent share in Markovic to the Premier League runners-up for €12.5million on Tuesday.
Liverpool have now confirmed that they have bought the player outright, after he passed a medical and agreed personal terms at Anfield.
The 20-year-old had long been linked with a move to the Merseyside club after an impressive season at the Estadio da Luz.
Markovic moved to Benfica from Partizan last June, and played a major role as the Lisbon club completed a domestic treble by winning the Primeira Liga, Taca de Portugal and Taca da Liga.
However, the versatile forward missed Benfica's UEFA Europa League final defeat to Sevilla after being sent off for his involvement in a touchline fracas in their semi-final win over Juventus.
Anfield boss Brendan Rodgers will hope Markovic's arrival at Anfield can help offset the loss of Luis Suarez, who is set to sign a five-year contract with Barcelona this week.
An estimated £75m deal has been agreed between Liverpool and the Catalan giants, though Suarez will be unavailable to play for Barca until late October after being hit with a four-month global ban for biting Giorgio Chiellini.
