The business secretary has also responded to the revelation that the woman accused of killing Harry Dunn in the MP's constituency used to be a CIA officer.
On HS2, which will go through south Northamptonshire, the Conservative MP said: "I know this will disappoint many of my constituents.
"But I can assure them that the prime minister has taken into account my concerns for constituents."
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Boris Johnson announced the approval of the multi-billion-pound train link between London, Birmingham, Manchester and Leeds in the House of Commons.
Phase one of the Department for Transport's (DfT) scheme, scheduled to be completed by 2040, is due to pass Brackley, Sulgrave, Chipping Warden and Upper Boddington.
HS2 was due to cost £56 billion in 2015 but that figure could now rise to £88 billion, according to the National Audit Office.
Supporters argue it will improve transport times, create jobs and boost the economy but its critics point to rising costs, allegations of mismanagement and the environmental impact.
Mrs Leadsom continued: "A minister will be appointed to oversee the project who will report to Parliament twice every year to hold HS2 properly to account.
"My priority, as it has been for the last 10 years, will continue to be making sure that affected constituents receive fair compensation and mitigation.”
Meanwhile, Harry Dunn's family wants a public inquiry into the 'scandal' surrounding the Northamptonshire teenager's death after it was revealed Anne Sacoolas used work for the CIA.
The American woman's history may help to explain why her government refused to extradite her to face her charge of causing death by dangerous driving over the crash near Croughton.
In response, Mrs Leadsom said: “The torment that the Dunn family continues to face is awful.
"I’m in regular contact with the family and with the foreign secretary and we all feel the same - that justice must be done and that Anne Sacoolas should return to the UK to stand trial.”
Harry, 19, died in hospital after his motorcycle was involved in a collision with Sacoolas' Volvo, which she has admitted was on the wrong side of the road, on August 27.
She initially co-operated with police but then told officers she had diplomatic immunity before flying back to the States a few weeks later, refusing to come back.
The Home Office asked the US State Department to send Sacoolas back after being charged by the Crown Prosecution Service but the Americans rejected the request.