The Cameroonian veteran is understood to have undertaken a medical with the Merseysiders, with personal terms also thought to be all but agreed.
The Toffees have surged into pole position for the veteran African over the course of the past few days, with bitter cross-city rivals Liverpool having switched their focus away from the 33-year-old to snap up Mario Balotelli.
Reports suggest that Eto’o could be Everton’s highest paid player, although his contract is highly incentivised and will include the option for a second year.
Roberto Martinez is thought to see him as great cover for Romelu Lukaku, with Arouna Kone’s injury absence having left the £28m man with little in the way of back-up.
Eto’o spent last season with Chelsea, but was released after one campaign in west London.
He has since been linked with lucrative moves to sides in the Middle East, but staing in England ins understood to have long been his aim.