Health charities have welcomed the bill, which will be subject to consultation for the next six months.
Action on Smoking and Health said it would help create a country where young people would never start smoking.
“It is important to have the debate about how we will protect children and vulnerable people from the harms of second-hand smoke,” said the charity’s chair, Prof Nick Hopkinson.
He added: “A key next step is for the government to set out further how it will help the UK’s six million smokers to quit. This will require a properly funded plan, paid for by a levy on tobacco companies.”
Dr Charmaine Griffiths, British Heart Foundation chief executive, said she welcomed the government’s commitment to protect children and vulnerable people from second-hand smoke in schools, playgrounds and hospital grounds.
“We also welcome measures to make vaping less appealing to young people,” she said.