The 27-year-old signed for Palace from Queens Park Rangers in 2020 for around £20m and went on to make 169 appearances, scoring 40 goals and providing 28 assists.
QPR will receive around 15% of the profit from the transfer, netting them an initial £6m.
Eze etched his name into Palace folklore by scoring the winner in last season’s FA Cup final against Manchester City, delivering the club’s first major trophy and ending a 120-year wait for silverware.
(Image: PA) Last season, Eze hit top form in the run-in, registering 25 goal contributions in 43 appearances for Oliver Glasner’s side – with only seven of those coming before Christmas.
He also became the first Palace player to score for England in 49 years when he netted against Lativa in March.
Announcing his departure on Instagram, Eze posted: "Five years, man. Crazy. It feels like just yesterday I was walking through the doors joining from QPR. The day you gave me the chance to realise my dream of playing in the Premier League, For South London’s biggest club.
"From the start, I had goals set and my targets in place for what I wanted to achieve here at Palace but I had no idea of what these last 5 years would really turn out to be.
"They call us a family club because it’s impossible to truly understand what it’s like to be part of this club unless you’re in it. They’re not wrong.
"Throughout the challenges of the covid times, from the day I tore my achilles and the long road of recovery to that night at Selhurst against Villa when I came back, up until this very day, the love you have all shown me, the way you have all supported me, and how we’ve stood together no matter what, these are things that will live in my heart forever.
"And thats all before we made history together, lol. Wembley, man. That whole journey. Words aren’t enough to describe what we all experienced that day so I’m not gunna try, but what I will say is that God did something for us that will connect us for generations.
"The most special day of my career because God gave us what no one thought was possible for us! So after all of this, all I really want to say is thank you. Thank you for believing in me, thank you for giving me a chance, and thank you for the love shared that will last a lifetime."
Speaking in his press conference on Friday, Palace boss Oliver Glasner said: "Ebs struggled last year at the beginning of the season but going through this period helped him become a better footballer.
"I spoke very often about the crunch time, I'm a big NBA fan and in the crunchtime the superstars are always on the court.
"When we needed Ebs in the crunch time, he was there. That's what I will always remember, with great players, when you need them they are always there.
"Great players never hide, we could count on Ebs in the very important games, this is what he gave to the team and to Crystal Palace."
Palace chairman Steve Parish added: “Throughout five years here, Eberechi has been an incredible presence, having had a huge impact on Crystal Palace Football Club and been an inspiration for the people of South London.
"Eberechi's journey is truly incredible: from being released from multiple clubs, to scoring the Cup final-winning goal, and helping bring the club its first major trophy in 164 years, he is a huge inspiration and role model.
"Just as importantly, and no less inspirationally, Ebs is a great person, always positive, always a positive presence, and humble in his dealings with everyone, regularly giving his time to the club's charity and other philanthropy. He epitomises everything good about the modern footballer.
“We, as a club, will always hold Ebs in our hearts and wish him all the success for the future. He will always be welcome back at Selhurst Park.”
Eze is due to be presented to the Arsenal fans at the Emirates Stadium ahead of their Saturday night clash against Leeds United and will wear the number ten shirt for the Gunners.