The deal, which is expected to be completed by the end of April, is worth approximately $1.1 billion, while under the terms of the agreement, Prudential will provide life insurance and pensions products to the three million Egg customers in the UK for the next five years.
In addition, Prudential will provide life insurance to Citigroup's consumer banking customers in Thailand, Indonesia and the Philippines.
The Prudential's group chief executive Mark Tucker said: "The sale of Egg to Citigroup realises greater value for our shareholders than retaining the business within the group.
"Citigroup is the largest credit card issuer in the world and sees enormous opportunities to develop Egg's business in the UK," he added.
The online bank was launched in the UK in 1998 and, despite initial successes, grew to be a loss-maker for Prudential following a failed attempt to expand operations into France.
Operating losses for Egg in the previous year are reported to be about $200 million, before tax.