Trevor Bickford - who was also charged with two counts of attempted assault - travelled to NYC by train from Maine before the attack, police said.
US media reported his family recently told the FBI they feared he was being radicalised by Islamist extremists.
Police Commissioner Keechant Sewell said the attack was "unprovoked".
The three officers - one of whom suffered a fractured skull after being struck by the machete - were all released from hospital on Sunday.
