The custom sparked a furious row between Wenger and Jol in April
The Premier League has asked players, managers and referees to end the custom of the ball being kicked out of play when a player goes down injured.
Decisions on whether a break in play is necessary for treatment to be received will now be taken by the referee.
"There was a general feeling that this player-led convention had gone too far," Premier League spokesman Dan Johnson told BBC Sport.
But the Football League told BBC Sport it had no plans to make changes.
The custom has gradually established itself in football over the years, but has never been formalised in the rules.
But the feeling that this "gentlemen's agreement" was being taken advantage of has become widespread, with frequent breaks in play at the 2006 World Cup cited as the most high-profile abuse.
Managers and players complained of situations where the ball was kicked out for non-existent injuries in order to stop a team's attacking momentum.
And the arbitrary nature of the convention has led to several flashpoints in recent years.
Last season, Arsenal's crucial Premiership match against Tottenham was marred by scenes of managers Arsene Wenger and Martin Jol squaring up on the sidelines.
Sheffield United's players walked off the pitch after the controversial goal
Wenger was furious when Spurs did not put the ball out of play after Emmanuel Eboue and Gilberto Silva were injured in the build-up to Robbie Keane's goal.
Another example of the misunderstanding the convention can produce is Marc Overmars' goal for Arsenal against Sheffield United in their 1999 FA Cup fifth-round tie.
In that instance, the ball had been kicked out by United to allow their player Lee Morris to receive treatment.
But instead of returning the ball to the Blades on resumption of play, Arsenal striker Kanu released Overmars to score.
The incident led to the match being replayed, with the Football Association agreeing to the Gunners' offer to play the match again.
WHY DID THE PREMIER LEAGUE WANT THIS CHANGE?
Premier League spokesman Dan Johnson:
"There were certain incidents - like the Martin Jol and Arsene Wenger flare-up last season - that made us think it was time to place the decision back in the hands of the referee.
"Sometimes the demand for the ball to go immediately out - from both players and fans - was almost acting as an extra defender.
It's important for the integrity and honesty of the game
Premier League spokesman Dan Johnson
"If there is a serious injury then the referee can, of course, take immediate action in the interests of player safety, but if it's a run-of-the-mill knock then play should go on.
"It's never been part of the rules, so that makes it all the more important to get the League Managers' Association (LMA) and the Professional Footballers' Association (PFA) on board.
"We need both organisations' support to communicate this to their members - and fans also need to be aware.
"This will remove the pressure on players who are wondering at the back of their mind 'is he really injured?'
"What people don't like to see is when an attack gets stopped because someone goes down grabbing their knee and then, a minute later, he's sprinting around and putting tackles in.
"It's important for the integrity and honesty of the game, as well as the flow."
WILL THE PFA CO-OPERATE?
PFA chief executive Gordon Taylor:
"I was at a meeting on Tuesday with the LMA and referees' representatives and lots of managers said they were confused and frustrated by the current state of affairs.
It's about striking a balance between common sense and player safety
PFA chief executive Gordon Taylor
"From that point of view, it's vital to establish some clarity so everyone knows exactly what the situation is.
"If the ball is kicked out then it should be a normal throw-in, and if the referee stops play, then when play restarts with a drop ball possession should return to the injured party.
"Player safety has to be paramount. We don't want referees mucking about if there's any doubt - they can't take any chances because players can, for instance, swallow their tongue.
"It's about striking a balance between common sense and player safety.
"Some people have been rather cynical about this custom, and that is what we want to lose - but without losing the spirit of fair play."
WHAT ABOUT THE FOOTBALL LEAGUE CLUBS?
Football League spokesman John Nagle:
"We will not be issuing any additional advice to referees, clubs or players regarding the issue of kicking the ball out of play at injury situations.
"There is no evidence that this convention is being widely abused within the League.
"We will, though, continue to monitor the situation."
WHAT DO THE MANAGERS THINK?
LMA deputy chairman Frank Clark:
"We've had several meetings with managers from all divisions and there is a huge majority in favour of giving the decision to the referees.
"It worked very well for a number of years, but you only had to watch certain matches at the World Cup to see it's being abused now.
We definitely think a change is the way forward
LMA deputy chairman Frank Clark
"Teams aren't giving the ball back in the spirit originally intended anymore and the whole thing's a mess.
"It's not a rule change, but because it's a convention which is ingrained in the game here, we need everyone on the same wavelength.
"To a certain extent, it's going to be a PR exercise, especially in terms of the fans.
"We definitely think a change is the way forward."
DOES THE FA HAVE A ROLE TO PLAY?
FA spokesman Andrin Cooper:
"There's obviously nothing in the laws of the game about it; it has just evolved over time.
"Our view is that if the referees, clubs and managers agree on one clear approach, then we're fine with that.
"If the participants affected - that is the players, managers and referees - agree, then it is absolutely down to them.
"In terms of grassroots football, I think we need to see how things progress in the professional game before any firm decision is taken."