Under terms of the deal, IBM will manage ABN's information-technology infrastructure, including data centers for ABN's commercial, consumer and private clients. The contract will be handled by IBM's Global Services division.
Four other companies will also share in the contract, worth a total of $2.2bn.
Amsterdam-based ABN Amro plans to shift around 2 000 tech jobs to IBM, and others under contracts.
ABN also intends on cutting another 1 500 jobs from its rolls.
Separately, IBM said it had finalised its acquisition of DWL, a privately held company that makes software that companies use to tie together customer information located at different locations within a company.