Mr Hancock said it was a “sensible and reasonable step” and he would consult on extending it to the NHS.
There are no plans to extend mandatory vaccinations beyond health and care workers, he said.
Workers will have 16 weeks to get both jabs from the time regulations are approved by Parliament.
If they do not, they face being redeployed away from front-line care or potentially losing their job.
Read more from the BBC here.