The Nigerian striker joined the Toffees aged 10 before rising through the ranks at Goodison Park under the Scot.
However, his long association with the club came to an end on transfer deadline day when he penned a deal with the Baggies.
"David Moyes has been such a help for me. He has been like a father figure," Sky Sports News quotes Anichebe as saying. "He brought me through when I was just a boy and he has stuck with me through thick and thin.
"It was a wrench (to leave) and there were moments even when I was driving down when I thought, 'is this the right decision?'. It was difficult but I thought it was the right time to leave."
Anichebe scored eight goals in 32 games for Everton last season.