Mr Johnson said the move was being taken "cautiously" and was based on the "latest data" for Covid-19 available.
The plan will see schools open on March 8 before a gradual lifting of other lockdown rules which will see other sectors reopen.
Stuart Anderson, MP for Wolverhampton South West, said: "My approach to lockdown has always been that I don't want to be back in this situation again.
"Residents, families, people working from home – everyone – have found it really hard and because it's been over the winter month, it's stretched everyone.
"But I want a slow release which prioritises the safety of individuals and to protect life – which is still the most important thing about this.
"We need to protect jobs, and the economy, but the priority at the moment is the schools – the schools have to open first and then, in the coming months, there's a gradual return to some form of normality.
"I definitely don't support the 'open all the gates' approach [to lifting lockdown] – I'm for a phased approach focused on the health and wellbeing of people.
"Then we can, at a safe pace, get the economy going again – but not at the expense of life or people's safety."
John Spellar, MP for Warley, welcomed the news but raised concerns for businesses – including pubs – which has led him to call on the Government for more support.
He said: "This is welcome progress, but with the rapid roll-out of vaccines, we need to be getting businesses back – otherwise many of them face permanent closure because they can't sustain continuing losses.
"I think there needs to be support [for pubs] now they're moving to vaccinate the over 50s – they [the Government] should urgently look at the question of a 'vaccine passport' to enable pubs to open as soon as possible, otherwise many of these pubs – which are community hubs – will not be there when the Government finally lifts the restrictions."
Michael Fabricant, MP for Lichfield, said: “This announcement will be of huge relief to millions. But the Prime Minister is right to be cautious. Unlike Rocky IV, lockdown four will not be as welcome.
"As we advance from one stage to the next, it will only be when it’s been shown to be safe to do so. So the dates which have been announced are the start dates when changes may take place and people should not be too surprised if they are delayed by a week or two.
"But I’m looking forward to visiting one of the many pubs in Lichfield with my friends and hope it will not be too long before it actually happens.”
Shaun Bailey, MP for West Bromwich West, welcomed the decision and said the focus could now return to “rebuilding” livelihoods and jobs in the Black Country.
He said: “Obviously, the Prime Minister has taken a cautious approach – as he said – because he wants this lockdown to be the last and I support that. The key thing is now is we have a phased approach that can allow people’s livelihoods, especially those in the Black Country, to pick up again.”