Under the new rules, passed by the governing body at its annual general meeting on Thursday, a panel will review footage from the weekend each Monday looking for cases of simulation.
Any player unanimously found guilty of diving would be given a suspension.
The FA also announced it has passed reforms it proposed in March, following criticism over the way it is run.
How will the new bans work?
The FA defines the new offence for which players will be punished as “successful deception of a match official”.
The panel will consist of one former match official, one ex-manager and one ex-player.
Only incidents that result in a penalty, a red card, or a yellow card that leads to a dismissal – either the first or second of two yellow cards – will be punished.
The FA says it will act “where there is clear and overwhelming evidence to suggest a match official has been deceived by an act of simulation, and as a direct result, the offending player’s team has been awarded a penalty and/or an opposing player has been dismissed”.
The announcement follows what the FA describes as “a period of consultation with stakeholders over the past few months”.
The rule change also required approval from the Premier League, the EFL and the Professional Footballers’ Association.
Speaking in December, Burnley manager Sean Dyche said he thought diving would be eradicated from football “in six months” if retrospective bans were introduced.
Such bans have been in place in Scottish football since 2011.
