The 38-year-old was Sean Dyche's first signing as Toffees manager last summer and became the club's oldest-ever outfield debutant before establishing himself as a first-team regular last season.
Young made a total of 34 appearances for Everton across all competitions, including 27 Premier League starts, and showed his versatility in a variety of wide roles.
The veteran scored his only goal of the 2023-24 season in a 3-0 EFL Cup win over Burnley and helped Everton avoid relegation from the Premier League, with Dyche's side securing 15th spot.
Young was due to see his original contract on Merseyside expire at the end of this month, but he has opted to commit his future to Everton for another season.
Young lauds "excellent" Everton fans after penning new deal
"It was a no-brainer for me to sign again," Young told evertontv. "I spoke to the manager before the end of the season. He asked me what I wanted to do, if I wanted to stay, and straight away I said yes because I loved my time here. Kevin [Thelwell] was the same.
"The size of the club, the staff, the players and, of course, the fans, who have been excellent... I loved my time here last season. We had ups and downs but I can see how big the club is and where the club wants to get to. I want to be a part of that.
"I'd put it up there with the best dressing rooms I've been in, with the best team spirit. There's a bond there. You can tell players have been here for a while, players who have played under the manager, players who know the club - just a real togetherness. Everybody is so close-knit, not just players but staff, as well.
"You feel that from the minute you walk in in the mornings to the time you leave. You feel that when you go to Goodison Park and when you're with the fans. There's a proper connection. I looked at that week [in April] and you heard how loud the fans are all the time. It was just something incredible. It was fantastic to be involved in.
"The way the club and the players took me in straight away from day one - I've just loved my time here. I'd already said about two months into the season that if there was an opportunity to stay for longer then I definitely would because it's a tremendous place to be."
Dyche pleased to secure future of "important figure" Young
Everton boss Dyche, who captained Young when they were teammates at Watford, added: "We're pleased to have secured Ashley's future for next season. His qualities - both on and off the pitch - meant he was an important figure for us.
"He's someone I've had the pleasure of knowing for many years and his depth of experience, leadership and versatility will undoubtedly help us again heading into next season."
Director of Football Thelwell continued: "Extending Ashley's stay with us was a relatively straightforward process because all parties were keen to get it sorted.
"He will continue to make a significant contribution, both on the pitch with his performances and also helping to guide many of our younger players in the squad."
The news of Young's contract renewal comes less than 24 hours after Everton confirmed that Jack Harrison has re-joined the club on loan from Leeds United for the 2024-25 campaign.
Everton have also completed the signing of 20-year-old midfielder Tim Iroegbunam from Aston Villa for a reported £9m.