UBS made the announcement on Tuesday as it confirmed a second-quarter pre-tax profit of 690 million francs, around one third more than in the same period last year.
The bank said the planned buy-back would bolster its capital in the fourth quarter of this year.
The move draws a line under the Swiss government's rescue of UBS nearly five years ago.
At the time the country’s biggest bank faced collapse over more than $50 billion in losses on mortgage securities.
The central bank’s fund was set up to bail out UBS at the height of the financial crisis.
The government took a nine percent stake in UBS as part of the bailout comprising six billion francs of equity and a loan from the Swiss National Bank (SNB).
UBS spun off $38.7 billion of risky assets into the fund.
Under the agreement, UBS was granted an option to buy back the equity of the fund once the SNB loan was fully repaid.
UBS last week announced its quarterly profit would exceed analysts’ expectations, even after paying $885 million to settle a lawsuit in the United States.
The news sent shares to a two-year high.
"The results show that our strategy is right and we're ahead on execution," UBS's Chief Executive Sergio Ermotti said in a statement on Tuesday.
Although UBS was cautious in its outlook it expressed confidence that its wealth management businesses would continue to attract new money.