Both players came through the ranks at Hamilton before reuniting for several seasons at Wigan.
McCarthy sealed a switch to Palace last summer, and McArthur is delighted to playing with his old friend once again.
"From about 10 years ago we've always had this understanding of each other," the Scot told the club's website.
"From Hamilton to Wigan, to play at this level at three different clubs has been some journey for both of us. Working with him is very natural, even when moving from club to club; as soon as we play with each other, we know what the other is going to do.
"For instance, James, whenever he loses the ball he goes after it straight away. I'll be there right after he gets back into position. He knows what I do when I lose the ball so we're always in a good position to help each other."