The crime of "insulting" someone through words or behaviour, which once led to the arrest of a student for asking a police officer whether his horse was gay, is to be dropped.
Home Secretary Theresa May confirmed to MPs that the government would not seek to overturn a Lords amendment scrapping the ban.
The director of public prosecutions has said it will not hinder his work.
But Labour warned that it could remove protections for minority groups.
Section 5 of the 1986 Public Order Act currently means that "threatening, abusive or insulting words or behaviour" might be deemed a criminal offence.
It has been strongly criticised by free-speech campaigners, and in December the House of Lords voted by 150 to 54, a majority of 96, to remove the word insulting.
The move was championed in the upper chamber by former West Midlands chief constable Lord Dear.
Mrs May told MPs: "I respect the review taken by their Lordships. They had concerns which I know are shared by some in this House that Section 5 encroaches upon freedom of expression.
"On the other hand, the view expressed by many in the police is that Section 5 including the word insulting is a valuable tool in helping them keep the peace and maintain public order.
"Now there's always a careful balance to be struck between protecting our proud tradition of free speech and taking action against those who cause widespread offence with their actions."
She said the government had supported the retention of the word insulting to prevent people swearing at police officers, protesters burning poppies, or "similar scenarios".
Ahead of the Lords vote, Director of Public Prosecutions Keir Starmer wrote: "We are unable to identify a case in which the alleged behaviour leading to conviction could not properly be characterised as 'abusive' as well as 'insulting'.
"I therefore agree that the word 'insulting' could safely be removed without the risk of undermining the ability of the CPS to bring prosecutions."
Mrs May said that, following Mr Starmer's intervention, ministers were "not minded" to challenge the Lords amendment to the Crime and Courts Bill.
But shadow home secretary Yvette Cooper pressed the government to produce an "assessment of the impact of Section 5 of the Public Order Act on different groups, particularly on minority groups".
"Many people have said that the existing Section 5 has formed some sort of protection," she told MPs.
"It is important to make sure we can protect freedom of speech but it is also very important to make sure we can protect vulnerable groups from unfair discrimination."
Campaigners say that different interpretations of the word insulting have led to spurious arrests, such as the arrest of a teenager for holding a "Scientology is a dangerous cult" placard.
Simon Calvert, campaign director for the Reform Section 5 group, said: "This is a victory for free speech.
"People of all shades of opinion have suffered at the hands of Section 5. By accepting the Lords amendment to reform it, the government has managed to please the widest possible cross-section of society. They have done the right thing and we congratulate them."