The deal was originally announced in October, when the companies said IBM would buy all shares in Red Hat for $190 each in cash.
For those who don’t know, the acquisition of the open-saucy, enterprise software maker, was IBM's largest deal ever and one of the biggest in US tech history.
It follows the $67 billion deal between Dell and EMC in 2016 and JDS Uniphase's $41 billion acquisition of optical-component supplier SDL in 2000.
Under the deal, Red Hat will now be a unit of IBM's hybrid cloud division, according to the original announcement.
The companies said Red Hat's CEO, Jim Whitehurst, would join IBM's senior management team and report to CEO Ginni Rometty. IBM previously said it hoped its acquisition of Red Hat will help it do more work in the cloud, one of its four key growth drivers, which are also social, mobile and analytics.
The company is behind Amazon and Microsoft in the cloud infrastructure business. IBM has seen three consecutive quarters of declining year-over-year revenue. But some analysts are hopeful about the Red Hat deal's opportunity to bring in new business.