Anne Sacoolas was charged with causing the 19-year-old's death by dangerous driving last month.
Harry died after his motorbike crashed into a car outside RAF Croughton in Northamptonshire on August 27 last year.
The 42-year-old suspect, the wife of a US intelligence official, claimed diplomatic immunity after the collision and was able to return to her home country, sparking an international controversy.
Now, the Home Office has said the matter is now "a decision for the US authorities" after formally submitting the extradition request on Friday.
Confirming the extradition request, a spokesman for the Home Office said: "Following the Crown Prosecution Service's charging decision, the Home Office has sent an extradition request to the United States for Anne Sacoolas on charges of causing death by dangerous driving.
"This is now a decision for the US authorities."
However the US has described the extradition request as "highly inappropriate".
A US state department spokesman said: "Under the circumstances of this case, we strongly believe that an extradition request would be highly inappropriate."
Reacting to the extradition request on behalf of Harry Dunn's family, spokesman Radd Seiger told the PA news agency: "This will not of course bring Harry back, but in the circumstances of all that this family have been through, they are pleased with the development and feel that it is a huge step towards achieving justice for Harry and making good on the promise that they made to him on the night he died that they would secure justice for him.
"Despite the unwelcome public comments currently emanating from the US administration that Anne Sacoolas will never be returned, Harry's parents, as victims, will simply look forward to the legal process unfolding, as it must now do, confident in the knowledge that the rule of law will be upheld.
"They will simply take things one step at a time and not get ahead of tthemselves. However, no one, whether diplomat or otherwise, is above the law."
Mr Seiger said he was "100%" sure Sacoolas would return to the UK.
He added: "There is no doubt in my mind and... there never has been.
"Whether it's today, or tomorrow, or in five years' time or in 10 years, Anne Sacoolas will come back, she has to come back."
The US State Department said an extradition request would be highly inappropriate, and insisted that Ms Sacoolas had status at the time of the incident that conferred diplomatic immunity.
A spokeswoman said they expressed their deepest sympathies and offered condolences to the Dunn family for their loss, and would continue to for options for moving forward.
"This was a tragic accident, a young man has lost his life, and his family is grieving. No-one could hear about this tragic accident and not feel incredible sadness over this loss.
"The president, the secretary of state, the US ambassador in London, and others in our government have all expressed sincere condolences to the Dunn family for this tragedy.
"The United States has been clear that, at the time the accident occurred, and for the duration of her stay in the UK, the driver in this case had status that conferred diplomatic immunities."