A big chunk of the proceeds - due before the end of 2015 - will be distributed to shareholders, mainly in the form of buy-backs. Shares opened more than 3% higher as BP also announced an improved quarterly dividend.
Its overall charge relating to the Gulf of Mexico disaster in 2010, which left 11 workers dead and sparked the worst oil spill in US history, stood at £26.4 billion at the end of September, but this was little changed on three months earlier.
The London-based company has benefited from a recent ruling by a US federal appeals court that the terms of a compensation agreement struck with BP last year should be reviewed to help stem bogus or inflated claims.
Underlying profits for the three months to September 30 were £2.3 billion, a fall of 26% on a year earlier but better than City forecasts for a decline of 37%.
BP set aside £5 billion for shareholders earlier this year as part of proceeds from the reshaping of the oil giant's Russian business. And it previously sold assets worth £23.6 billion to pay for the Gulf of Mexico spill.