The 24-year-old Nigerian set off for Merseyside after the two clubs agreed the fee on Wednesday afternoon as the long-running transfer saga took a decisive twist.
The Teessiders confirmed they had agreed an undisclosed fee with the Toffees and had given them permission to speak to the Nigeria international.
A Boro spokesman said: "We can confirm we have agreed a fee for the sale of Yakubu and he has been given permission to talk to Everton.
"We will only confirm the fee once any deal is complete."
However, Everton later revealed the magnitude of their offer - a club record - in a statement on their website, evertonfc.com.
It said: "Everton can confirm that they have agreed a club record transfer fee of £11.25 million with Middlesbrough for the transfer of Yakubu.
"The Nigerian international centre-forward is now travelling to Merseyside for talks with The Toffees."