Terms of the deal, which is expected to close in second quarter of this year, weren't disclosed.
The acquisition is part IBM's Smarter Commerce initiative, which is designed to help businesses automate and infuse more analytics and intelligence into their procurement, marketing, sales and customer service.
The company has invested $2.5 billion since 2010 in the initiative.
San Francisco-based Tealeaf provides management software that records and analyzes a customer's website and mobile interactions with customers. The company's customers include the likes of Dell, Wells Fargo and Expedia.
IBM employs thousands in the Triangle and is one of the region's largest technology employers.