Changes to the laws of the game take effect from July 1, although IFAB said competitions have the flexibility to introduce them sooner.
The amendment is an about-turn on a law announced two years ago by the IFAB.
Fifa president Gianni Infantino said the panel felt that "after analysing everything" disallowing goals automatically on basis of handball "was going one step too far... in terms of the spirit of the laws of the game generally".
A latest controversy relating to the current, stricter rule was fresh in English Premier League side Fulham fans' minds after a goal by Josh Maja against Spurs on Friday was ruled out when the ball cannoned into the hand of his team-mate Mario Lemina from a Davinson Sanchez clearance.
Fulham boss Scott Parker hit out at the law after his team's 1-0 defeat, saying: "I understand why the goal was not given and that's the rule. I don't agree with the rule. I am not complaining with that, the referee is acting to the rule.
"We have Var so you can look back and see if there is a clear advantage. I don't think we did. We are trying to make the game so pure and sterile and trying to control every single phase or moment to an absolute T and that is where the problem lies."
IFAB also opened the door to the use of five substitutes being extended through the 2022 World Cup.
The congested calendar due to the pandemic saw competitions last year permitted to give teams two additional substitutions in matches. That currently runs through July 2022 for national team competitions but IFAB said it will "remain under review."
- with the Daily Telegraph UK