The Crime and Policing Bill would also introduce CCE prevention orders - which would allow courts to put restrictions on people who they believe pose a risk of exploiting a child for criminal purposes.
Set to be introduced to Parliament next week, the Crime and Policing Bill would explicitly make the two acts illegal and introduce restriction orders on those thought to be using children for criminal means.
The Home Office said the proposed CCE offence is designed to target people who groom children into criminal activity such as county lines drug dealing or organised robbery.
Ms Cooper added in a statement: "These steps are vital in our efforts to stop the grooming and exploitation of children into criminal gangs, deliver on our pledge to halve knife crime in the next decade and work towards our overall mission to make our streets safer.".
Child criminal exploitation (CCE) and "cuckooing" will be made new offences under a new law, the home secretary has said.
