They were arrested in August a year ago after MI5 bugged the auto of Naweed Ali and uncovered a pipe bomb and meat cleaver hidden in a JD Sports bag.
Ali, Rahman and Hussain had referred to themselves as the "Three Musketeers" while communicating via encrypted messaging service app Telegram.
Naweed Ali, 29, Khobaib Hussain, 25, and Mohibur Rahman, 33, hatched the plan involving meat cleavers and a pipe bomb between May and August a year ago.
Jurors agreed with him and, after deliberating for more than 22 hours, unanimously convicted the men of preparing terrorist acts, along with fourth defendant Tahir Aziz, 38.
Ali, Hussain and Rahman were arrested on August 26 and police monitored their communications.
Ali, Hussain and Rahman met while serving prison terms for terrorism offences, prosecutors said.
Family man and Primark salesman Aziz was keen not to be "left behind" but was only brought into the Three Musketeers plot days before the arrests.
MI5 and undercover police officers had set up a fake firm in the city called Hero Couriers which employed both Hussain and Ali.
The defendants were also covertly photographed meeting on a boating lake and in a park days before their arrests, the court heard.
Two days later, Ali arrived for his first shift at Hero Couriers and left his Seat Leon auto at the Birmingham depot before MI5 moved in to conduct a search and "technical" operation - bugging the vehicle.
But after a four-month trial, held in secret, a jury today convicted them of plotting a mass casualty terror attack in the UK.
His DNA was also found on a strip of tape used to strap an empty magazine onto an imitation hand gun inside the the JD Sport bag found in his auto.
Police immediately arrested all four men and seized a large sword which had been stashed in Aziz's vehicle.
Prosecutor Gareth Patterson QC said the attack the men had planned "would be in the UK" but said that prosecutors did not need to identify the target, adding: "It is clear that attacks could be carried out imminently".
In the bag was the meat cleaver and half-made pipe bomb.
Mr Justice Globe remanded them in custody until sentencing on Thursday morning.
The three men were arrested in August a year ago but they insisted "Vincent" had planted the weapons in the vehicle to frame them.