The agreement is for an enterprise value of up to £2.025 billion including a £200 million contingent consideration, with RBS keeping a 19.99% stake in the business.

RBS will get around £1.7 billion in cash on closing of the sale of the 80.01% interest and up to another £200 million in the future if the returns realised by the consortium members exceed certain thresholds.

The bank says the deal - to close before the end of the year - will result in a gain of around £850 million after goodwill, separation and transaction costs.

RBS was told to sell off WorldPay - or Global Merchant Services - by the European competition authorities last year as a condition for joining the UK government's asset protection scheme.

It received over a dozen offers for the world's fourth largest provider of card payment services, with private equity groups, payment processors and IT vendors all in the frame. The field was gradually narrowed down before Advent and Bain entered into exclusive talks on a deal at the end of last month.

Established in 1989, WorldPay processed a total of 6.8 billion transactions last year. The business operates in over 30 countries and has the ability to process up to 680 transactions per second in 113 currencies across 72 payment methods.

With electronic transactions increasingly taking over from cash and cheques, the industry is seen as a potentially lucrative market by PE firms. The RBS deal comes just a year after Advent acquired a 51% stake in the payments processing business of Fifth Third Bancorp.

Ron Kalifa, already part of the business, will act as chief executive officer.

James Brocklebank, head, financial services sector, Europe, Advent, says: "WorldPay is a unique business and we are delighted to be supporting Ron Kalifa and his team in the next phase of its growth. Advent and Bain will be making a very significant investment in the company to enhance its technology and expand the range of products and services offered to merchants."

Bruce Van Saun, group finance director, RBS, says: "The sale of GMS is another significant milestone in the Group's restructuring programme. GMS is an excellent business. The transaction will be good for both staff and customers as the business implements its ambitious expansion plans."

The WorldPay sale comes on the same day RBS posted a small first half net profit of £9 million, compared to a £1.04 billion loss for the same period last year. Operating profit for the six months was £1.6 billion.

Earlier this week the bank also completed the sale of 318 UK branches - on European competition authority orders - to Spain's Santander for £1.65 billion.