Zebroski, 28, pleaded guilty to four charges relating to two incidents at Swindon Crown Court.
His club responded by terminating his contract.
The court heard that he crashed his BMW into a taxi last December and attacked another taxi driver who was filming him when he got out of the car and tried to take his mobile phone.
He also assaulted and attempted to rob two men in February.
Rob Ross, defending, said Zebroski had a problem with alcohol. The court heard he had previous convictions for assault and alcohol-related incidents.
Recorder Ian Lawrie said: “Whatever talent you had as a footballer has been squandered because of alcohol abuse.
“It is a matter of regret if this sentence shatters your professional football career.”
The League Two club later confirmed that they had terminated his contract.
In a statement the club said: “The club have always had the welfare and wellbeing of Chris at heart and have worked hard with Chris and the PFA throughout.
“However, we would like to make it clear that we do not condone any of the actions for which Zebroski has been found guilty.
Regrettably, the club are left with no other option than to terminate Chris’ contract. Newport County will not be making any further comment on the situation.”