Posh chairman Darragh MacAnthony revealed the news on his official Twitter account and Boyd will now discuss personal terms with Palace.
MacAnthony tweeted: "We have agreed terms with Crystal Palace for the transfer of George Boyd tonight. 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.
"We have had nearly 7 years of Boyd talent to enjoy & I hope he now gets to strut that talent in Prem next year if he does leave Posh."
Boyd, 27, joined Peterborough from Stevenage for £260,000 in January 2007 and has since made almost 300 appearances for the club.
Meanwhile, Peterborough have cancelled the contract of left-back Scott Griffiths by mutual consent.