Inter Milan will have the option to buy the Croatia international at the end of the loan deal.
Vrsaljko started six of Croatia's seven games at the World Cup, including the final.
According to the BBC, the fee is thought to total £21.34m.
Vrsaljko is returning to the Serie A after spending three seasons with Genoa and Sassuolo, between 2013 and 2016.
He will join Ivan Perisic and Marcelo Brozovic at San Siro.
Some reports have also suggested that Inter could be looking into signing Luka Modric.