Gulam Chowdhury, 24, from Barking, was convicted of murdering Mohammed Yasser Afzal at the Old Bailey.
Mr Afzal, from Forest Gate, was killed outside a cab office in Broadway, Stratford, in March 2014.
Police said Chowdhury, of Heenan Close, had plotted to kill Mr Afzal because of a row over a woman they had both been in a relationship with.
The court heard the woman had told Chowdhury that Mr Afzal had compromising pictures of her on a mobile phone.
Police said he was threatening to expose their relationship to her parents, who did not approve.
Mr Afzal was working at E20 Cars when he was stabbed 20 times in the attack on 24 March. He never regained consciousness.
Officers managed to place Chowdhury at the scene of the murder through mobile phone records.
Det Insp Euan McKeeve said: "The level of violence used was shocking and ensured that Mohammed would not survive the attack.
"Whatever Mohammed's motives were for the actions he took in attempting to maintain his relationship with a woman, he did not deserve to be murdered."
Another man - Mohammed Khan, 24, of Lindsey Road, Dagenham - was found not guilty of assisting an offender.
The jury was discharged having failed to reach a verdict over charges against Nargis Riaz, 22, from Barking, who was accused of murder. She denied the charge.
Correction 23 April: The verdict in the case against Mohammed Khan has been amended in light of a clarification from the court.
A man has been found guilty of stabbing a minicab dispatcher to death in east London.