Video footage from the scene shows Mr Trump dropping to the ground clutching his right ear after multiple bangs were heard ringing out.
In a statement, the organisation said: “The FBI has identified Thomas Matthew Crooks, 20, of Bethel Park, Pennsylvania, as the subject involved in the assassination attempt of former President Donald Trump on 13 July, in Butler, Pennsylvania.
“This remains an active and ongoing investigation.”
It is understood the gunman behind the assassination attempt was a registered Republican, according to the Associated Press.
Crooks was registered with the party in Pennsylvania, where the shooting occurred.
The former US President stays on the ground for several moments before rising to the feet, protected by agents forming a human shield.
Mr Trump is ushered off stage by the agents when he tells them to ‘wait’, before raising his fist several times and seemingly shouting ‘fight’.