Video footage appeared to suggest the Hull substitute spat in Hart's direction after the goalkeeper had reacted furiously to Boyd's fall under his challenge in the box in the 69th minute.
Referee Lee Mason booked Hart for his part in the incident, and Boyd for diving in the penalty box, however the FA have decided not to take any further action against Hart for his part in the confrontation.
Boyd has until 6pm on Wednesday to respond to the charge, which relates to an incident which was not seen by referee Mason.
An FA statement said: "Hull City's George Boyd has been charged by the FA following his side's game against Manchester City on March 15, 2014.
"The charge is in relation to an alleged breach of FA Rule E1 [a] in that in or around the 68th minute of the game, Boyd spat at Manchester City's Joe Hart. The incident was not seen by the match officials but caught on video.
"Boyd has until 6pm on March 19, 2014 to respond to the charge.
"Under a new pilot project in Premier League matches this season, if an incident has not been seen by the match officials, a three-man panel of former elite referees will be asked by the FA to review it and advise what, if any action, they believe the match referee should have taken had it been witnessed at the time.
"For an FA charge to follow, all three panel members must agree it is a sending-off offence. In this instance, the panel were of the unanimous decision that it was an act of misconduct."