From August 16, anybody who has had two doses of a vaccine or is under the age of 18 will not be subjected to ten days at home if they get close to somebody who has tested positive.
As under-18s are not routinely jabbed, the exemption from self-isolation rules will be extended to them.
Announcing the change, Health Secretary Sajid Javid told the House of Commons that “we must balance the risks” of the virus against social and economic impacts.
He told MPs “We will soon be able to take a risk-based approach that recognises the huge benefits that the vaccines provide both to people who get the jab and their loved ones too.
“So from 16 August when even more people will have the protection of both doses, and when modelling suggests the risks from the virus will be even lower, anyone who’s a close contact of a positive case will no longer have to self-isolate if they have been fully vaccinated."
Mr Javid says that anybody who gets their second dose near that date will have to wait two weeks before they can skip isolation, in order for the vaccine to take effect.
Anybody who is a close contact will be advised "to take a PCR test as soon as possible so they can get certainty about their condition," Mr Javid said, and anybody who tests positive will have to self-isolate, regardless of their vaccination status.
The change paves the way for the controversial bubbles policy in schools, - which has seen hundreds of thousands of children missing classes - to end.
Education Secretary Gavin Williamson told the Commons that from Step 4 of the Covid road map in England - currently anticipated on July 19 - bubbles will end, and acknowledged the "disruption" pupils and parents have experienced.
He told MPs: “I do not think it is acceptable that children should face greater restrictions over and above those of wider society, especially since they have given up so much to keep older generations safe during this pandemic.”
Responsibility for contact tracing in schools will be passed to NHS Test and Trace, and Mr Williamson also said that "all other existing measures – including guidance on isolation of contacts – will stay in place until the end of this term, in line with isolation rules for the rest of the population as more adults as vaccinated.
Mr Williamson told the House of Commons that other measures such as staggered start and finish times will also no longer be necessary but that "some protective measures – including enhanced hygiene and ventilation – will remain in place for the autumn term."
Under current rules, whole classes and nurseries have been sent home when one among their number tests positive.
According to figures from the Department for Education around 8.5% of state school pupils were missing from the classroom on July 1, including approximately 561,000 who were self-isolating due to a possible contact with a positive case.
In addition, another 34,000 were off with a suspected case of Covid-19, and 28,000 were confirmed to have tested positive.
The announcements come the day after the Prime Minister laid out the proposed ending of most restrictions in England if the country is able to move to Step 4 on July 19 as planned.