Byung Lin Lee, 32, of no fixed address, was charged with assault on a police officer and possession of a bladed article.
The Metropolitan Police say there was no danger to Mr Blair or his family, but a review was immediately launched into security measures around the prime minister.
It is also understood that the man's mental health will be assessed.
Lee allegedly scaled a 1.8 metre iron fence behind the building on Sunday night and was confronted by a police officer, whom he lunged at.
A brief scuffle ensued -- where Lee did not use his knife -- before he was pinned to the ground as other officers arrived. Police do not believe the incident was terrorist-related.
The most serious security breach ever on Downing Street was in February 1991 when the Irish Republican Army (IRA) launched a mortar shell into the back garden after parking a van in nearly Whitehall.
The mortar exploded, blowing out windows at the back of the building, while then prime minister John Major was conducting a cabinet meeting inside.