Armed with his victims' full names and details of their account and credit cards, Stewart phoned ANZ and Westpac call centres and "somehow by-passed the security processes in place", to con the customer service staff into giving him access to their accounts, Judge John Bergsens said.
"You were given sufficient access to change passwords with a telephone and internet bank account."
Stewart then set up a number of so-called 'mule accounts', and transferred "significant sums of money from the victim's accounts through to the mule accounts".
"These were then immediately withdrawn," Judge Bergsens said.
In total Stewart - a father-of-one - withdrew $160,328 of the more than $200,000 he transferred.
The scam had financial consequences for the two banks involved, Judge Bergsens said, on top of the stress and anxiety it had caused to staff.
In a victim impact statement, ANZ highlighted the "trauma and stress for those that have been cheated by your actions", the judge said.
Staff were "persuaded by you to allow you access to accounts", he said, telling Stewart he had "conned these people".
Stewart had racked up 48 convictions for dishonesty offences since 2006, prosecutor Duncan Coleman said, "and that doesn't include the current seven that he faces in court today".
"His criminal history, together with the current offences, conservatively paints him as an inveterate fraudster", Mr Coleman said.
Stewart's previous jail terms include time for burglary and theft, as well as a 2011 conviction for accessing a computer system for dishonest purposes.
Defence counsel Gerry Skinner said his client was "very remorseful", and had suffered from a drug problem which "underpinned all of this offending".
In a letter sent to Judge Bergsens, Stewart said he felt he had "hit rock bottom", in particular to the careless driving incident, in which he injured five people, including a 17-year-old girl who now has permanent damage to her ankle.
"You said for the first time in your life you were anti-'P', and want to make efforts to distance yourself from friends and associates that are still users, and make a better use of your life," Judge Bergsens said.
Addressing Stewart in the dock, he continued: "The reality for you is, if you don't make those changes, you're going to go through the same exercise as today except the sentence that will be imposed will simply become longer and longer and you will find you're spending the bulk of your life in custody."
Judge Bergsens sentenced Stewart to five years and nine months in prison as a cumulative sentence for all the charges he faced. He was also disqualified from driving for nine months.
Stewart was supported in court by his mother and her partner, nodding to them on a few occasions. His mother wiped her eyes with a tissue as he stood calmly in the dock.
