MacAnthony revealed on Twitter that Palace had matched the club's valuation and that the player will now discuss terms with the Eagles.
"We have agreed terms with Crystal Palace for the transfer of George Boyd tonight," MacAnthony tweeted. "The player will now talk terms with Palace.
"It's obviously sad news for us at Posh but we couldn't turn this opportunity down for the player. Many clubs have made bids which in truth were verging on taking the mick, however CP have backed their manager & met our terms today.
"George has been a Palace fan all his life & now has chance if he joins them to help them get promoted to Premier League."
Boyd has made 260 league appearances for Posh since joining from Stevenage in 2007.