"I know that I can develop and succeed in the Benfica team," the winger said on the web site of the Primeira Liga runners-up. No further details of the transfer were given.
Markovic will join his compatriots Nemanja Matic and Filip Djuricic at the Portuguese club. Matic arrived in Portugal in 2011 and was a revelation last season, while attacking midfielder Djuricic has recently signed from Dutch club Heerenveen for €6 million euros ($7.9 million, £5.1 million).
Portuguese media have linked Benfica with another Serbia international, 24-year-old forward Miralem Sulejmani, from Ajax.
Benfica were looking for a historic treble last season but were pipped at the post by Porto on the penultimate match of the season, then lost the UEFA Europa League final against Chelsea and Portuguese Cup final against Vitoria de Guimaraes.