But there will be strict controls on the numbers of people on each site, changes to what materials are accepted and revised opening hours.
Recycling centres were temporarily closed at the end of March following Government guidelines on non-essential journeys to help prevent the spread of the coronavirus.
From Monday, both Farnham and Witley CRCs will be open "for black bag waste and garden waste only" seven days a week; from 9am to 6pm in Rake Lane, Witley, and 9am to 4pm in Guildford Road, Farnham.
Residents are asked to hold on to other waste, such as card, wood, metal, electrical and construction waste – and there is an outright ban on vans, pick-ups, trailers and pedestrians.
Surrey’s intention is to move to a second reopening phase after a “few weeks” when the full range of materials can be accepted, but only when it is safe to do. Check for the latest information online at surreycc.gov.uk/recycling
All Hampshire sites will reopen from 10am to 4pm daily, but only for "essential disposal of waste whereby storing such waste causes a risk of injury or to health".
Unlike in Surrey, Hampshire’s tips will accept "all waste material streams" – but residents are advised to check www.hants.gov.uk/recyclingcentres before travelling to check if any specific material is not able to be accepted temporarily.
Trailers are also banned in Hampshire, but vans will be allowed providing they bring "no more waste than that which would fit in an average saloon car boot".
And Rob Humby, Hampshire’s executive member for the environment, has also confirmed number plate recognition will not be enforced at Hampshire’s recycling centres during this period.
County bosses have been under pressure to reopen waste facilities to avoid fly tipping, and councillors – including Surrey’s opposition Lib Dem group – have welcomed the move to reopen.
But both Surrey and Hampshire councils expect large queues to form as residents rush to dispose of excess waste.
Wyatt Ramsdale, Tory councillor for Farnham South, said: “It is good to see Farnham’s CRC opening again from Monday after it was closed following central government recommendations regarding essential services.
“But please don’t all try to go at once! We know how congested the site gets normally.”
To maintain social distancing, a reduced number of visitors will be able to visit recycling centres at any time – and "as far as possible" residents should go alone as only one person will be permitted to leave each car.
Residents in the shielding category (those who are clinically extremely vulnerable, people over 70 and pregnant women) are "strongly advised" not to visit a site.
Staff in both Surrey and Hampshire have been told they cannot help with unpacking cars, so if one person isn’t able to carry the waste, it should be left at home.
And in Hampshire, security staff complete with body cameras will be deployed at all sites to ensure the above restrictions are adhered to.
Hampshire has also warned "there will be a zero-tolerance approach to any form of abuse".
Reuse sites in Surrey and Hampshire will remain closed.
It comes after Andrew Joy, Hampshire county councillor for Alton Town and executive member for communities, confirmed plans were in place to reopen tips in his report to Alton Town Council last week.
He added the reversal of tip closures had been “held up” by government guidance, as journeys to community recycling centres are not currently deemed essential travel – but added the council was working with waste contractor Veolia to loosen up restrictions.