Benfica declared that the club has sold the 20-year-old's sporting rights and the 50 percent that the club owned of the forward's economic rights to the Reds for €12.5 million.
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Markovic becomes the Reds' fourth summer signing following the acquisitions of Emre Can from Bayer Leverkusen and Adam Lallana and Rickie Lambert from Southampton.
The Serbia international scored seven goals for Benfica last season, although he was not involved in the club's Europa League final defeat to Sevilla after he was sent off from the bench for a clash with Juventus's Mirko Vucinic in the semifinal.
The 2013-14 campaign was just his third in senior football, having made the move to Portugal in 2013 following two seasons for Partizan Belgrade.
He had been linked with a move to Chelsea before completing that transfer to Benfica and the Blues were said to have kept tabs on the diminutive right winger over the past 12 months.
Markovic completed a medical on Merseyside over the weekend and late on Monday night posted a series of pictures on his official Facebook page revealing that the move had been rubber-stamped ahead of the club's official confirmation.
Liverpool is keen to make a splash in this summer's transfer window as the club looks to reinvest following the sale of Luis Suarez.
The Uruguayan striker, banned from any football-related activity until the end of October, will complete a move to Barcelona this week after an €88.5 million deal was agreed between the two clubs.
Suarez, though, cannot be officially unveiled to the club's fans under the terms of his FIFA ban for biting Italy defender Giorgio Chiellini.
Liverpool is also in talks to sign Southampton defender Dejan Lovren and Lille striker Divock Origi, who made an impact at the World Cup for Belgium.