The 33-year-old, who has played 67 times for Jamaica, is reunited with former boss Steve Evans, who managed him at the Sussex club, and will stay at New York until the summer of 2014.
"We knew around tea-time on Sunday that Claude had made his decision," Evans said.
"It came down to two clubs from around six or seven that wanted Claude, and I think he limited himself to speaking to four of those clubs.
"It was never a surprise to me that he was in big demand, for a year and a half he was outstanding for me.
"Claude is man who will defend with his heart and he'll be a good signing at the right time for us."