The deals are expected to close by the end of January 2020.
The deals, which are the company's largest, build on VMware's strength helping companies run their software in their own data centres.
They could help VMware compete better in the security market and hybrid-cloud infrastructure operations.
CEO Pat “Kicking” Gelsinger said the companies will be operating profitably under VMware next year. Gelsinger said that by year two, Carbon Black and Pivotal will have contributed more than $1 billion in revenue incrementally, which will mean VMware will have more than $3 billion in hybrid cloud and software-as-a-service revenue.
Carbon Black was founded in 2002. The company provides anti-malware and endpoint protection products that can see into many of a company's devices and tell if they have been hacked.
Pivotal was spun out of VMware and Dell (VMware's controlling owner) in 2013. Its products help companies build and deploy their software across different server infrastructure, including public clouds.
Competitors include IBM, Oracle and SAP, among others, as well as cloud providers such as Amazon and Microsoft. Pivotal's customers include Boeing, Citi, Ford and Home Depot, according to its website.