Johnson will set out a roadmap to ease England's third national lockdown on Monday, having met a target to vaccinate 15 million Britons from higher-risk categories by mid-February.
Britain now aims to give a first dose to all over-50s by April 15, the government said, having previously indicated it wished them to receive the shot by May.
If all adults receive a dose by the end of July, it will be well ahead of a previous target that they would receive a vaccine by autumn.
After suffering the world's fifth-worst official COVID-19 death toll and a series of mishaps in its pandemic response, Johnson's government moved faster than much of the West to secure vaccine supplies, giving it a head start.
Johnson cautioned that there was a need to avoid complacency, adding that lockdown would only be lifted slowly.
"We will now aim to offer a jab to every adult by the end of July, helping us the most vulnerable sooner, and take further steps to ease some restrictions in place," Johnson said in a statement.
"But there should be no doubt - the route out of lockdown will be cautious and phased, as we all continue to protect ourselves and those around us."
So far, the United Kingdom has given a first dose of vaccine to 17.2 million people, over a quarter of its 67 million population and behind only Israel and the United Arab Emirates in vaccines per head of population.
Two vaccines - one made by Pfizer and BioNTech, and another developed by the University of Oxford and AstraZeneca - are being rolled out, and UK officials have advised that there can be a 12-week gap between doses.