From February, EDS will help Bank of America, the third-largest bank in the US, transform its voice and data network systems, the companies said in a joint statement.
IEDS will also redesign and install Bank of America's optical network and provide the company with customer help desk services.
"It is important for us to capitalise on the expertise of partners like EDS to help us align our resources with business needs, " said Don Obert, technology services executive at Bank of America.
Coley Clark, president of EDS's financial global industry solutions group, said the outsourcing deal would "provide consistency and predictability" to Bank of America's infrastructure.
The deal is EDS's first multibillion-dollar contract since September, when it issued a shock profits warning after problems with two major contracts and cuts in corporate spending on computer services.
Since then, EDS has lost out on major contracts with US bank JP Morgan and household goods giant Procter & Gamble.
Clark told CW360 that EDS hoped to sign a £1bn IT outsourcing deal with ABN Amro, Holland's largest bank, by the end of the year.
The outsourcer is in exclusive talks to provide technology services to Bank of Bermuda as part of a 12-year, $375m deal.
EDS is also is negotiating on a major desktop services outsourcing contract with Barclays Bank.