The move is in line with two trends at Citigroup, the largest US bank by assets.
Chief executive Charles Prince has eschewed blockbuster deals and, instead, focused on targeted and strategic acquisitions. In December, Citigroup announced it was buying Quilter, a wealth management unit in the United Kingdom, from Morgan Stanley; at the same time, it bought a Central American banking company in a stock-and-cash deal.
Citigroup also has been moving in recent years to expand its online presence. Its US retail banking arm launched Citibank Direct in March to offer high-yield savings accounts to compete with similar offerings from other Internet banks and to attract more people to its online-banking and bill-paying services.
Ajay Banga, chairman of Citigroup Global Consumer Group-International, said that Citi hopes to capitalize on Egg's reputation for a consumer-friendly website and strong brand recognition.
He said that Egg's strength has been its "ability to deal with online customers in a way that makes them happy and sells them other products as well."
Citi, he said, can bring its expertise to improve Egg's less-than-impressive lending record and to provide new products, including checking accounts and investments such as mutual funds.
Banga also said Citi could apply what it learns to its Internet operations in other countries.