The former Barnsley starlet had the choice between a move to the Latics under Roberto Martinez or the Toffees back in January 2013.
Despite opting against joining the Spaniard at the DW Stadium over a year ago, Stones is delighted that he is now working under the 40-year-old on Merseyside.
He told The Express: "I was driving up to Wigan while my agents were there as I had been at training at Barnsley in the morning. I got the call to say the bid had been accepted, then later on I had another call to say that Everton had also had a bid accepted.
"It was a decision for my career. Everton was the right move for me. I let Roberto know and he accepted it. I remember having to go into his office on the first day. It was a strange feeling being at Everton, yet having him as my manager.
"He said, 'We are together now, we are at the same club, so let's move forward from here.' It was a good feeling."
Chelsea and Arsenal are among those understood to be keen on signing the 19-year-old this summer.