The 28-year-old refused to return to Stamford Bridge after being allegedly informed by manager Antonio Conte via text message that he was no longer wanted.
With preferred destination Atletico Madrid unable to register players until January due to a FIFA transfer ban, Costa was faced with the prospect of getting no game time until the New Year.
According to talkSPORT, Everton tabled a bid worth around £66m for the Spain international, with Toffees boss Ronald Koeman looking for reinforcements up front.
However, the report suggests that Costa had his mind set only on joining the La Liga side, a wish that has now come true following a £57m deal being agreed between Chelsea and Atleti on Thursday.
Costa scored 59 goals in 120 games for Chelsea and helped the West Londoners to two Premier League titles.