The penalty, agreed with US, UK and Swiss regulators, is more than three times the $450 million fine levied on Britain's Barclays in June for rigging the Libor benchmark rate used to price financial contracts around the globe.
It is the second-largest fine paid by a bank and comes a week after Britain's HSBC agreed to pay the biggest ever penalty - $1.92 billion - to settle a probe in the US into laundering money for drug cartels.
In a statement, UBS chief executive Sergio Ermotti disclosed the extent of the wrongdoing, which took place from 2005 to 2010.
"We deeply regret this inappropriate and unethical behaviour," the statement said.
"No amount of profit is more important than the reputation of this firm and we are committed to doing business with integrity."
UBS said it would pay $1.2 billion to the US Department of Justice and the Commodity Futures Trading Commission, 160 million pounds ($247 million) to the UK's Financial Services Authority (FSA) and 59 million Swiss francs ($61 million) from its estimated profit to Swiss regulator Finma.
The FSA said at least 45 people were involved in the rigging, which took place across a range of Libor currencies.
A similar admission by Barclays in June touched off a political firestorm that forced its chairman and chief executive to quit.
The Libor benchmarks are used for trillions of dollars worth of loans around the world, ranging from home loans to credit cards to complex derivatives.
Tiny shifts in the rate, compiled from daily polls of bankers, could benefit banks by millions of dollars. But every dollar a bank benefited meant an equal loss by a bank, hedge fund or other investor on the other side of the trade - raising the threat of a raft of civil lawsuits.
The steep fine for UBS is despite the bank, since 2011, cooperating with law enforcement agencies in their probes.
The bank said it received conditional immunity from some regulators.
UBS has had a tough 18 months after suffering a $US2.3 billion loss in a rogue trading scandal, management upheaval and thousands of job cuts.