The tournament, starting on 28 June, will begin with 50% ground capacity.
That will then rise throughout the tournament before the two finals on the 15,000-capacity Centre Court.
Wimbledon is being treated as fan pilots – exempt from strict capacity limits despite the government’s decision to delay the easing of all remaining coronavirus restrictions until 19 July.
Culture Secretary Oliver Dowden said: “We want to gather further evidence on how we can open up all big events safely, and for good.
“The expansion of trials of the NHS app and lateral flow testing will mean that bigger crowds will be able to attend a limited number of major sporting and cultural events early this summer as part of our events research programme.
“In the next few weeks, this means more fans enjoying the Euros and Wimbledon, and some of our biggest cultural and sports events.”
At Wimbledon, the women’s singles final takes place on 10 July and the men’s singles final is on 11 July.
“We are continuing to work closely with the Government to finalise the details including the requirements for Covid-status certification for spectators,” the All England Club, which organises the tournament, said in a statement.
“We are pleased to have worked closely with the government, public health bodies, and our local authority in Merton, to confirm that, as part of this next phase of pilot events, the Championships 2021 will begin on Monday 28 June with 50% capacity across the grounds, building to full capacity crowds of 15,000 on Centre Court for the finals weekend.
“This will enable us to fulfil our aspiration of staging the best Wimbledon possible within the current circumstances, with the health and safety of all those who make Wimbledon happen – our guests, competitors, members, staff, media, officials, local residents, and partners – remaining our highest priority.”