Kweku Adoboli, once a rising star City trader, was found guilty by a London court of the biggest fraud in British history.
At one point, he had stood to run up losses of £7.5bn for his employer.
The 32-year-old admitted to the bad trades, but denied any wrongdoing.
He wiped away tears as he sat in a glass dock at the back of the courtroom while the jury delivered the verdict.
Adoboli was convicted of two counts of fraud by abuse of position linked to the £1.4bn loss, but jurors cleared him of four counts of false accounting between October 2008 and September 2011.
Judge Mr Justice Keith, sentencing, told Adoboli: "There is a strong streak of the gambler in you. You were arrogant enough to think the bank's rules for traders did not apply to you."
"The fact is you are profoundly unselfconscious of your own failings."
He sentenced Adoboli to seven years for one count of fraud and four years for the other, to be served concurrently.
Adoboli will serve half the sentence before being released on probation, and -- taking into account the time he has already spent behind bars -- he could be out of prison in about two and a half years.
In a statement, UBS said: "We are glad that the criminal proceedings have reached a conclusion and thank the police and the UK authorities for their professional handling of this case."
Adoboli maintained during the two-month trial that senior managers had been fully aware of his activities and had encouraged him to take risks to make profits for UBS.
Giving evidence in tears last month, he said he viewed his UBS colleagues as "family" and had acted for the good of the bank.
The multi-billion-dollar deals happened at a time when he was suffering from burnout and had "lost control" of his trading, he added.
But prosecutors painted a different picture, saying Adoboli had exceeded his trading limits, failed to hedge trades and faked records to cover his tracks in a bid to boost his status and ego.
They said he saw himself as having a "magic touch" as a trader.
Prosecution lawyer Sasha Wass told jurors he was "a gamble or two away from destroying Switzerland's largest bank for his own gain".
"Mr Adoboli's motive for this behaviour was to increase his bonus, his status within the bank, his job prospects and, of course, his ego," she said.
Ghanaian-born former public schoolboy Adoboli joined UBS as a graduate trainee in 2003 and, at the time of the fraud, was a senior trader on the Exchange Traded Funds desk at UBS' investment banking arm in London.
He was arrested in September 2011 after he confessed his losses in an email to colleagues.
The police inspector who investigated Adoboli called him "one of the most sophisticated fraudsters the City of London Police has ever come across".
Behind the façade of a man whose career appeared to be taking off "lay a trader who was running completely out of control" and a "young man who wanted it all and was not willing to wait", Detective Chief Inspector Perry Stokes said.
The Crown Prosecution Service said the case, behind all the technical jargon, ultimately rested on whether Adoboli had acted dishonestly.
"He did so, by breaking the rules, covering up and lying," said Andrew Penhale, deputy head of fraud at CPS.
"At the heart of any complex fraud is a simple notion of dishonesty which is something that we can all understand."
Also attending the session was Adoboli's father John, who has travelled to London from Ghana to support his son throughout the trial.