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.
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.
The England international also became the first Palace player to score for the Three Lions in 49 years when he netted against Lativa in March.
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."
Confirming Eze's departure, Palace Chairman Steve Parish said: “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.