The government will introduce the change as part of the Queen's Speech in Parliament in early June to enforce the protection of children's emotional, social and behavioural well-being.
Parents found guilty under the law could face up to 10 years in prison, the maximum term in child neglect cases.
It follows a campaign for a "Cinderella Law" by the charity Action for Children.
Its chief executive, Sir Tony Hawkhead, said: "This is a monumental step forward for thousands of children who we know suffer from emotional abuse and countless others whose desperate situations have yet to come to light.
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Hawkhead added: "We are one of the last countries in the western world to recognise all forms of child abuse as a crime. Years of campaigning have been rewarded - the government has listened and this law will change lives."
Robert Buckland, a Conservative MP who has backed the charity's campaign, said the current law was outdated as it is based largely on legislation first introduced 150 years ago.
"Isolating them, belittling them, rejecting them, corrupting them, as well, into criminal or anti-social behaviour," he said, adding that the new law would not criminalise parents for being nasty, but for their criminal behaviour.
Currently in the UK, the criminal definition of child neglect, which affects as many as one in 10 children, covers physical harm only.