The fee hasn’t been officially confirmed but earlier reports suggested Everton will pay in the region of £6m for the 17-year-old, who had just a year left on his contract at St James’ Park.
Gibson has signed a three-year contract at Goodison Park and will link up with David Unsworth’s U23 squad.
The left-sided central defender was a regular for Newcastle’s U18 side last season and was later promoted to the reserve side after a string of impressive performances.
Gibson also earned a call-up to the England U17 squad and was an ever-present as the Young Lions reached the final of the U17 European Championships earlier this summer.
This latest signing will bring to five the number of additions that David Unsworth will have to work with at the Under-23 level this season. Defender Nathangelo Markelo, striker Boris Mathis and winger Josh Bowler have all been signed this summer with forward Anton Donkor coming back on another loan spell.
Dutch youngster Joshua Zirkzee has also reportedly joined the club, though the deal has yet to be officially confirmed.
This latest deal demonstrates Everton’s continued commitment to developing their U23 side that lifted the Premier League 2 title last season.
Speaking about the move to the official website, Gibson said:
"Everton is a brilliant club and when the opportunity presented itself I wanted to be part of it.
"The reputation has long been there that Everton brings through young players. You only have to look at the likes of Tom Davies, Kieran Dowell, Jonjoe Kenny and several others who are battling for first-team places to know this.
"I'm a player who is willing to put my body on the line, the kind of defender who likes to tackle and is not afraid. I'm excited to be part of things here and I want to continue developing as a player. This is where I want to be.”