The deadline, which had been extended until 31 May previously, was only applicable to those who had a reservation agreed prior to 30 June 2020.
As applications for the scheme ended on 15 December 2020, the extension only applies to those who have already had begun proceedings.
Homes England has outlined that this will be the final extension it grants.
If a development is unable to complete by 31 May 2021, homebuilders will be forced to release buyers from their contract.
As well as this, homebuilders will be required to refund reservation fees if buyers do not go ahead with buying the home.
If the buyer has exchanged contracts, the homebuilder must also return their deposit.
Furthermore, applications can be made under the Help to Buy equity loan, which begins from 1 April 2021.
Homes England said: “We are extending legal completion to 31 May 2021 due to delays caused by coronavirus.
“This allows an extra two months for homebuilders to complete the build and for homebuyers to legally complete and get the keys to their home.
“There will be no more extensions, so we are asking homebuilders to continue to build at pace.”
Craig Hall, head of broker relationships and propositions at Legal & General Mortgage Club, added: “COVID-19 has disrupted and even delayed the construction of new homes, including those available through Help to Buy.
“However, the government’s decision to extend the legal completion date of Help to Buy to 31st May will provide a much-needed breathing space for consumers to finalise their home purchase before the current scheme ends.
“It’s been confirmed that this will be the final extension of the scheme and advisers now have a key role to play in helping buyers to understand what these changes mean for them.
“The wider mortgage industry, including advisers, lenders, surveyors and conveyancers, must now work together to ensure those using the current Help to Buy programme are able to complete on their purchase as quickly as possible.
“Importantly, with the current stamp duty ‘holiday’ due to end on 31 March, those unable to complete before this date will need to pay the associated stamp duty on their property, although first-time buyers in England will remain exempt up to £300,000.
“Tapering the ‘holiday’ deadline could help avoid this cliff edge – something we hope policymakers will consider in the forthcoming Budget.”