The contract, expected to be finalised later this year, calls for EDS to provide a variety of IT services to ABN AMRO's Wholesale Clients unit, including management and development of applications, said John Clendening, an EDS spokesman.
The Wholesale Clients unit, one of the bank's three main divisions, is devoted to major international corporations and institutions. This division has about 10,000 clients and a staff of around 22,000 in over 45 countries.
By outsourcing IT tasks, the bank expects to lower costs and gain flexibility, said Hans van Zon, an ABM AMRO spokesman.
If finalised, the contract would be EDS' largest contract this year. About 17% of EDS' $21.5bn (£14bn) revenue last year came from financial services clients.
EDS already provides IT services to the bank, but this would be by far their largest engagement, both in terms of the scope and value of the project.
Of the about 3,000 IT staffers at the Wholesale Clients unit, around 1,000 would be transferred over to EDS as part of the deal, ABN AMRO's van Zon said.
ABN AMRO has assets of more than $620bn (£406.4bn) and around 110,000 employees.