The 19-year-old played against Everton in their recent Europa League qualifier and impressed Ronald Koeman enought to sanction a seven-figure move.
The deal for the striker is thought to be worth in the region of £8m, thought it is thought that the Croatia U21 international could be sent straight back out on loan, much like fellow new signing Henry Onyekuru.
Vlasic has made 85 appearances for Split since making his deubut in July 2014, scoring 10 goals in the process.
The signing of Vlasic would push Everton's summer spending past thh £150m mark.
Hajduk president Ivan Kos left the door open to a move for the youngster at the weekend when he told local newspaper Slobodna Dalmacija: "The transfer window runs until August 31, sometimes transfers happen a minute before midnight...We also have to think about financial stability."