The Croatia international is currently undergoing a medical at the Toffees' Finch Farm training complex ahead of discussing personal terms with the Merseyside outfit.
Goal.com's Chief Correspondent Wayne Veysey understands that Everton have not only matched Rangers’ £7 million valuation of the striker, but will also double the player’s wages, boosting his current £20,000-a-week deal to £45,000.
Championship side West Ham United, who were also in the hunt for Jelavic’s signature, were not prepared to match either figure.
Jelavic will become the third signing by manager David Moyes, after the Scot brought in duo Darron Gibson and Landon Donovan earlier this month.
After moving from Rapid Vienna back in the Summer of 2010, Jelavic has netted 36 goals in 55 appearances for the Glasgow side, with manager Ally McCoist not keen to see the striker depart Ibrox.
The 26-year-old’s move will be aided by the departure of midfielder Diniyar Bilyaletdinov, who left Goodison Park late last week for Spartak Mascow, in turn allowing Moyes some room for manouevre in the transfer market.