Vlasic spent last season on loan at Torino and has been vocal about re-joining them in the ongoing transfer window.
The Italian club’s decision to not take up the €13m option on him and the subsequent haggling over a fee with West Ham has dragged out the negotiations.
The midfielder has been pushing West Ham to agree to let him go and following weeks of talks, a deal is now in place between the two clubs.
According to Turin-based daily Tuttosport (via Tutto Mercato), the two clubs have reached a broad agreement over a fee and the structure of a deal.
The Hammers have agreed to accept the latest offer from Torino, which is a €10m fixed fee and another €2m in add-ons.
The Italian club have also agreed to pay a percentage of any future sale proceeds to West Ham as part of a deal.
West Ham and Torino are now working on the final details of the deal for Vlasic’s move to Turin this summer.
The midfielder has already agreed personal terms on a contract worth €2m per year and has been training in Milan while waiting for the green signal to join Torino.