The 24-year joined the Toffees from Burnley on Monday in a deal worth £25m.
However, in recent months, Keane had linked with a return to his former club, Manchester United.
"Of course it was a temptation [to join Manchester United] - it's your boyhood club," Keane told the club's website.
"But you have got to take your heart out of it sometimes and think what's best for you, and I feel as if this [Everton] is the best place for me to come and continue my development.
The Red Devils youth product moved to Burnley for just £2m in 2015.