The 21-year-old, who joined Everton as an 11-year-old, has moved to St. James' Park for an undisclosed fee after Everton rejected an initial £40 million offer for the player last week.
"Since I heard of the interest, I was always convinced Newcastle were for me," Gordon, who signed a long-term deal, said. "I think the fan base and the city really suits me as a person, the way the team are playing under the gaffer at the minute really suits me, and the club just look like they're heading in the right direction.
"I feel like it's a really big step. People haven't seen what I'm capable of yet. I think under the gaffer, and the way the club's going, I can really excel here."
Gordon will not be able to make his Newcastle debut in Tuesday's Carabao Cup semifinal second-leg against Southampton -- Newcastle lead 1-0 from the first-leg -- after becoming cup tied while playing in Everton's third round defeat against Bournemouth in November.
"I'm delighted to sign Anthony -- he's a top, top talent," Newcastle head coach Eddie Howe said. "I'm really excited to work with him, to develop him, and I'm looking forward to seeing what he can do in a Newcastle shirt."
ESPN reported earlier this week that Gordon failed to report for training at Everton amid interest from Newcastle, who are chasing a top-four finish in the Premier League and Champions League qualification.
The England Under-21 international leaves Everton with the club 19th in the Premier League and fighting relegation for a second successive season.
Everton rejected two offers of £40m and £45m from Chelsea last August, but the player has endured a difficult season at Goodison Park, scoring just 3 goals in 18 appearances for the club.
He was subject of intense criticism from Everton supporters on social media following the 2-1 home defeat to relegation rivals Southampton earlier this month, accused of laughing at fans who were protesting outside Goodison Park.
The sacking of manager Frank Lampard has left the club searching for a new coach to take charge in time for the home game against Premier League leaders Arsenal on Feb. 4.