Michael Sandford, 20, from Dorking, Surrey, was accused of trying to grab a police officer`s gun to shoot Mr Trump at a Las Vegas rally on 18 June.
He pleaded guilty to being an illegal alien in possession of a firearm and disrupting an official function.
His plea means he could be deported and his sentence reduced.
Sandford previously pleaded not guilty to charges of disrupting government business and official functions, being an illegal alien and possession of a gun and had been due to stand trial later this month.
He may have faced up to 20 years in a US prison if he had been convicted at trial. He is due to be sentenced on 13 December.
At a court in Nevada, he acknowledged he had been treated in the past for mental illness.
Entering his pleas, he said: "I tried to take a gun from a policeman to shoot someone with, and I`m pleading guilty."
His mother Lynne Sandford and the family`s UK lawyer visited him in jail for the first time last week to persuade him to sign the plea agreement.
Mrs Sandford said: "Even though he has signed the plea agreement, which should be the best option, it won`t necessarily happen that way.
"The judge at sentencing can either agree with what is in the plea bargain or he can totally overthrow that and impose a punishment of his own."
She added that her son told her he was "incredibly sorry and remorseful for everything," adding: "Everybody says this is not him - this is so opposite to what he is."
Sandford`s lawyers said he suffers seizures, obsession-compulsion anxiety and autism spectrum disorders.
His mother said he was recently diagnosed as having had a psychotic episode at the time of the incident and should serve any sentence in a UK psychiatric hospital.
Briton pleads guilty on Trump gun charges
14 September 2016
Read: 979
A British man accused of trying to shoot US presidential candidate Donald Trump has pleaded guilty to some of the charges he faced.
