However, the Sussexes won't make an "immediate decision" about whether they will attend.
The spokesperson said: "I can confirm the duke has recently received email correspondence from His Majesty's office regarding the coronation. An immediate decision on whether the duke and duchess will attend will not be disclosed by us at this time."
The news follows months of speculation about whether Harry and Meghan will make an appearance at the landmark ceremony that will see Charles officially crowned as King.
The couple's team are understood to be publicly addressing the email invitation after The Sunday Times was briefed by palace aides that it had been sent and reached out to them for clarification.
Confirmation of an invitation comes just days after the news broke that Harry and Meghan have been evicted from their UK home of Frogmore Cottage, which was given to them as a gift by Queen Elizabeth, so that the keys could be offered to Prince Andrew.
The King is reported to be keen to move Andrew out of Royal Lodge – his long-term home, also located in Windsor Great Park – into the smaller Frogmore Cottage, which will be cheaper for the Duke of York to maintain when Charles stops his annual allowance in a few months.
One reason the decision to evict Harry and Meghan has been seen as so controversial is security – all the royal homes in Windsor Park are protected by the police.
The couple had their taxpayer police security removed when they stepped back as working royals in 2020, and Harry is currently in a legal dispute with the Home Office so that he can pay for police security himself when he visits the UK.
Last year, a representative for Harry said this was because the private security he uses in the US doesn't have the proper jurisdiction or intelligence required to keep the Sussexes safe in the UK – only the police have that.
The Mail on Sunday has reported that the couple may be offered a Buckingham Palace apartment to stay in as a type of "olive branch". If that's accurate, then the palace seems to be trying to quickly course correct so any bad relations with the Sussexes don't end up overshadowing the coronation itself.
Watch: The real story of the Royal Family's dysfunctional life behind closed doors