A "terrible" loophole will be closed from next week, ministers said, by extending the offence of causing or allowing the death of a child in order to cover serious physical harm.
Police believe as many as 20 cases of child abuse, and three in which the victims were vulnerable adults, went unpunished in 2010 because of the gap in the existing legislation.
The new law comes into force on Monday after the Government made the rare move of backing a Private Member's Bill introduced by Sir Paul Beresford.
Kenneth Clarke, the Justice Secretary, said: "By making sure this Bill became law we have taken the opportunity to close a terrible loophole which has, until now, allowed people accused of seriously harming a child or vulnerable adult to escape unpunished.
"We want to do everything possible to ensure that the most vulnerable members of our society are kept safe in their homes, and those that abuse their power do not evade justice."
The offence of causing or allowing the death of a child or vulnerable adult was introduced to stop people, often parents, escaping prosecution if they blamed each other for the death of a child in the family home or refused to say what had happened.
Between 2005 and 2010 the offence was used to successfully prosecute 31 people, including Tracey Connelly, her boyfriend Steven Barker, and his brother Jason Owen. They were jailed over the death of Baby P, a toddler who suffered horrific neglect and abuse that was missed by doctors and social workers.
The Domestic Violence, Crime and Victims (Amendment) Act 2012 extends the offence to causing or allowing serious physical harm, such as inflicting brain damage or broken bones.
Sir Paul, the Conservative MP for Mole Valley, said: "After spending time with the Metropolitan Police I realised there were loopholes in the law that the Government could close to protect children and vulnerable adults.
"This new legislation will ensure that fewer cases of abuse slip through the net and is another safeguard to protect some of the most vulnerable members of our society."