The 28-year-old was seen entering the Toffees' Finch Farm training ground yesterday for the medical after the fee was agreed between both sides.
According to Sky Sports News, only a few details remain before the transfer is finalised and an official announcement is anticipated later today.
The England international has fallen out of favour at the Emirates this season and has not started a Premier League game for the club since last April.
Just two weeks ago Arsenal manager Arsene Wenger claimed that he was keen for Walcott to stay, but it is believed that progress on deals to bring in the likes of Pierre-Emerick Aubameyang from Borussia Dortmund and Manchester United's Henrikh Mkhitaryan have convinced the Frenchman to sell.
Walcott has been with Arsenal since the age of 16, having joined from Southampton in 2006.