The prime minister said the 10-year strategy for England and Wales would also tackle 2,000 county lines gangs.
The £300m gangs crackdown will be joined by the "largest ever investment in treatment", the government said.
Other measures include using dealers' seized phones to message clients and discourage drug use.
Speaking on a visit to Merseyside Police headquarters, Mr Johnson said:
"Overwhelmingly, the problem is caused by 300,000 people whose lives are simply chaotic, who are torn apart by their own addiction.
"You've got to help them, you've got to do treatment. But you've also got to come down hard on the county lines gangs."
County lines gangs are urban drug dealers who sell to customers in more rural areas via dedicated phone lines.
They are notorious for exploiting children to work as couriers and forcing vulnerable people to let them use their homes to conceal or deal drugs.
The government said operations targeting these gangs had led to the closure of 1,500 lines so far, with more than 7,400 arrests and more than 4,000 vulnerable children and adults safeguarded.
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