The 17-year-old, who has played for Wales at Under-17 level already, has been with the Toffees academy.
Morgan, who is very familiar with the Goodison Park club having been there since the age of seven, hopes he can make a first team claim in the coming years.
Morgan told evertontv: “It means a lot because it’s something I’ve been working towards since joining the Club.
“Being here so long, it’s great playing with your mates and improving. There’s a real togetherness and it’s like a big family.”
He added: “I feel like when I played last season, I developed a lot, but over the past two seasons I’ve had a few injuries so I just want a consistent run of matches.
“Being here since I was seven, eventually playing at the new stadium would be great. I want to play in the Premier League for Everton and be their main striker one day, so that’s the main target for me.”