Vlasic has been deemed surplus to requirement at the London Stadium just a year after his arrival from CSKA Moscow.
The Hammers are keen on offloading him this summer with Italian outfit Torino finally managing to get a deal over the line.
The Serie A side will take Vlasic on loan this season and will have the option to buy him for £15m at the end of the spell.
Vlasic will now fly to Italy in order to take part in his medical before finalising the move.
The Croatian had made it clear that Torino were the only club he was intent on joining with Napoli also showing interest in his services.
The Hammers had managed to snap the 24-year-old from CSKA Moscow last summer for a fee in the region of £30m including add-ons.
Over the course of his one-year stay, Vlasic managed to feature in 31 games for the Hammers scoring one goal and setting up two more for his team-mates.
