The two experienced midfielders will leave Selhurst Park on free transfers when their contracts expire next month.
Milivojevic joined the club in the summer of 2016 and has gone on to make 198 appearances, registering 28 goals and six assists.
With 28 of those goals taking place in the top flight, Milivojevic will depart Palace as their third-highest scorer in the Premier League.
"It has been a privilege to spend almost seven years at such a special club," Milivojevic told the Palace website. "I want to thank all of the managers, coaches and staff members who made my stay here such an enjoyable one.
"When I look at the club now compared to when I arrived, I see a team full of ambition to reach higher and higher - you can be sure I will be following the results from afar.
"To the fans: there is something special about Selhurst Park, and the way you got behind me on the field, whether we were winning or losing, is something I will never forget.
"To play in the Premier League is every player's dream, and to do it for so long at Crystal Palace has been an honour - I hope that I have made you all proud."
McArthur, meanwhile, has scored 19 goals and provided 23 assists in 252 appearances since joining Palace from Wigan Athletic in 2014.
The 35-year-old said: "If you'd have told me when I first came to Crystal Palace that I'd be here for nine seasons, I'd have found it hard to believe, because it's rare in football to spend so long at such an amazing Premier League club.
"I would like to thank everyone: all my managers, the Chairman (Steve Parish), Dougie Freedman (Sporting Director), and the players present and past.
"I've had a journey with so many people here over the years. I also want to say a massive thank you to every one of the fans.
"The support that I've had personally, and the support that they give the team, is like at no other club. When times are tough, Palace fans really get behind the team, and that's so important to all of us. I will always be a fan of the club."
Milivojevic and McArthur received the Chairman's Award for Outstanding Contribution from Parish at the club's End of Season Awards on Wednesday evening.