The compromise plan put forward by Michelle Donelan, the culture secretary, would hold tech bosses accountable "in a way which is effective and targeted towards child safety".
Social media bosses who ignore rules in place to protect children could be jailed after a climbdown by ministers to prevent a major backbench rebellion against Rishi Sunak over the Online Safety Bill.
The prime minister conceded to demands of around 50 Tory MPs who put their names to an amendment to the bill that would make tech chiefs criminally liable if they do not block minors from seeing damaging content.
In a written statement on Tuesday to appease the rebels, Michelle Donelan, the culture secretary, said the bill would be amended so that senior managers who "have consented or connived in ignoring enforceable requirements, risking serious harm to children" face criminal penalties.
She added: "The criminal penalties, including imprisonment and fines, will be commensurate with similar offences.
"While this amendment will not affect those who have acted in good faith to comply in a proportionate way, it gives the act additional teeth to deliver change and ensure that people are held to account if they fail to properly protect children."
The change - the third time Mr Sunak has backed down to appease rebels in his own party since he entered Number 10 in October - allowed him to avoid a potentially embarrassing defeat in the Commons as the bill went through its final stages.
It passed its third reading without a vote and will now head to the House of Lords for further scrutiny by peers.
Former cabinet ministers, including ex-home secretary Priti Patel and former Conservative leader Sir Iain Duncan Smith, were among those who backed the change.
During a debate on the bill in the Commons, Ms Patel thanked ministers for accepting that criminal liability for rogue social media bosses "had to be addressed".
"It is important that we get the right outcomes because all of us want to make sure that children are protected from some dreadful harms that we've seen online," she said.
Others warned the measures may go too far and questioned whether they would be effective.
Sir Jeremy Wright, the former culture secretary, said there were two fundamental problems with the amendment, the first being that it "potentially criminalises any breach of a safety duty" as it is drafted too broadly.
The second, he said "is the difficulty of prosecuting successfully the sort of offences that we may create".
He told MPs: "There is a strong case for extending criminal liability but I have to say I think new clause two goes too far."
The NSPCC has campaigned to have managers made criminally responsible for failing to offer protection to children.
Richard Collard, associate head of child safety online policy at the children's charity, said that Ms Donelan had "sent a strong and welcome signal that she will give the Online Safety Bill the teeth needed to drive a culture change within the heart of tech companies that will help protect children from future tragedies".
Labour said it supported the third reading of the legislation as "each day of inaction allows more and more harm to spread".
Referring to the government's climbdown, Alex Davies-Jones, the shadow culture minister, told the Commons: "The fact that we are seeing amendments withdrawn at the last minute goes to show that this government have absolutely no idea where they truly stand on these issues."
Lucy Powell, the shadow culture secretary, accused the government of having "failed to read the room" on the legislation.
"These concessions show the prime minister's weakness in having to roll over to vested interests and his fractious party to avoid defeats in the House of Commons," she said.
The prime minister conceded to demands of around 50 Tory MPs who put their names to an amendment to the bill that would make tech chiefs criminally liable if they do not block minors from seeing damaging content.
In a written statement on Tuesday to appease the rebels, Michelle Donelan, the culture secretary, said the bill would be amended so that senior managers who "have consented or connived in ignoring enforceable requirements, risking serious harm to children" face criminal penalties.
She added: "The criminal penalties, including imprisonment and fines, will be commensurate with similar offences.
"While this amendment will not affect those who have acted in good faith to comply in a proportionate way, it gives the act additional teeth to deliver change and ensure that people are held to account if they fail to properly protect children."
The change - the third time Mr Sunak has backed down to appease rebels in his own party since he entered Number 10 in October - allowed him to avoid a potentially embarrassing defeat in the Commons as the bill went through its final stages.
It passed its third reading without a vote and will now head to the House of Lords for further scrutiny by peers.
Former cabinet ministers, including ex-home secretary Priti Patel and former Conservative leader Sir Iain Duncan Smith, were among those who backed the change.
During a debate on the bill in the Commons, Ms Patel thanked ministers for accepting that criminal liability for rogue social media bosses "had to be addressed".
"It is important that we get the right outcomes because all of us want to make sure that children are protected from some dreadful harms that we've seen online," she said.
Amendment 'goes too far'
Others warned the measures may go too far and questioned whether they would be effective.
Sir Jeremy Wright, the former culture secretary, said there were two fundamental problems with the amendment, the first being that it "potentially criminalises any breach of a safety duty" as it is drafted too broadly.
The second, he said "is the difficulty of prosecuting successfully the sort of offences that we may create".
He told MPs: "There is a strong case for extending criminal liability but I have to say I think new clause two goes too far."
Change 'will help protect children from future tragedies'
The NSPCC has campaigned to have managers made criminally responsible for failing to offer protection to children.
Richard Collard, associate head of child safety online policy at the children's charity, said that Ms Donelan had "sent a strong and welcome signal that she will give the Online Safety Bill the teeth needed to drive a culture change within the heart of tech companies that will help protect children from future tragedies".
PM 'having to roll over to vested interests'
Labour said it supported the third reading of the legislation as "each day of inaction allows more and more harm to spread".
Referring to the government's climbdown, Alex Davies-Jones, the shadow culture minister, told the Commons: "The fact that we are seeing amendments withdrawn at the last minute goes to show that this government have absolutely no idea where they truly stand on these issues."
Lucy Powell, the shadow culture secretary, accused the government of having "failed to read the room" on the legislation.
"These concessions show the prime minister's weakness in having to roll over to vested interests and his fractious party to avoid defeats in the House of Commons," she said.