Currently the MP for South Northants, Mrs Leadsom, 53, is strongly against HS2, and has worked with Bucks County Council leader Martin Tett and campaigners who are fighting the scheme.
The pro-Brexit MP is being championed by one-time leadership frontrunner for the position Boris Johnson, which would see her become Prime Minister despite not standing at a general election.
On announcing her candidacy Mrs Leadsom, who was born in the town in 1963 to parents Judy and Richard Salmon, said: “The next Prime Minister must bring the nation together.
“The EU referendum didn’t cause divisions but it certainly did reveal them.
“Many people are shocked at the result but they really shouldn’t be.
“What I would like to say to them is please: Don’t be afraid; We haven’t lost our senses; We haven’t stopped caring about each other; We haven’t stopped loving our families and children; We haven’t stopped loving our country either; We’ve just rediscovered our Freedom!”