Solicitor General Robert Buckland QC had asked for a review of the 12 year jail term originally handed down to Nicholas Adair at Leeds Crown Court.
Adair, 28, of of Poole Crescent, Cross Gates, amassed a small fortune through selling cannabis, which he used to buy a house and a BMW for his partner.
He had been arrested previously for a number of drug offences, including one instance when police found Â£80,000 worth of cannabis in his home.
The attack for which he was jailed took place in February 2017 when Adair and another man got into an argument with two others in Harehills.
When victim Martin McDonagh tried to intervene in the argument, Adair struck him with a glass bottle.
Mr McDonagh was then dragged to the ground and stamped on, causing head injuries.
He managed to escape but Adair and the man he was with chased him in their car until they knocked McDonagh over.
As a result, Mr McDonagh lost part of his ear and sustained fractures to his ribs and spine.
The Court of Appeal today decided that Adair's sentence should be increased to 14 years in prison.
Speaking after the hearing, the Solicitor General said: “Adair’s crimes were truly despicable and he deserved to be in jail for longer.
"Not only did he violently attack Mr McDonagh, he also damaged his community through drug dealing.
"I am glad that the Court of Appeal agreed with me that his sentence was too low. I hope that Mr McDonagh will find some comfort in the ruling today.”