The two are long-serving members of the Selhurst Park outfit's squad.
McArthur joined from Wigan Athletic in 2014 and has racked up 252 appearances for the Eagles.
Club captain Milivojevic signed from Olympiacos in January 2017 and is Palace's third all-time top scorer in the Premier League with 28 goals.
The former Serbia international has taken in 198 appearances for Crystal Palace.
Chairman Steve Parish told the official club website: “We have been lucky to have a professional like Luka at the club for so long.
“He has contributed an immense amount to the team both on and off the pitch and is a crucial figure in our long stay in the Premier League.”
Milivojevic added: “It has been a privilege to spend almost seven years at such a special club.
“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 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.”
On McArthur, Parish added: “An absolute stand-out professional, on and off the pitch, James’ leadership and character will be hard to replace.
“I’d like to personally thank him for his contribution to the club and wish him and his family nothing but the very best for the future. We look forward to one day welcoming him back; he will always be welcome at Selhurst Park.”
McArthur 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.
“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.”