The announcement came later than expected, after promises that the deal would be completed by the end of last month.
Executives were eager to unveil the completion at the Red Hat Summit annual user conference in Nashville last week.
Red Hat first announced its intention to acquire Jboss in April, and is paying up to $420m in stock and cash for the open source application server vendor.
Red Hat plans to build out the Jboss products into a suite that enables service oriented architectures. Jboss has several products in this area, but its offering is far from complete.
Jboss founder and chief executive Marc Fleury has been appointed senior vice president and general manager of the Red Hat Jboss division.
The acquisition has raised concerns about the future of Jboss support on the Windows platform. About half of all Jboss customers run the software on Windows machines.
The take-over by the Linux vendor could bode ill for these users if the company determined the Windows customers to be dead weight.
Al Gillen, research vice president for system software at analyst firm IDC, believes that there is no cause for concern.
"By maintaining JBoss as a division, JBoss customers aboard other platforms should see continuity with the JBoss products they use," he said.
Both Red Hat and Jboss marketed an application server. The company will discontinue the Red Hat Application Server and merge the underlying technology with the Jboss product.
Dr Kuan Hon criticises GDPR consent emails that will only eviscerate marketing databases and 'media misinformation'
Apple squashes Steam Link app on 'business conflicts' grounds
Philip Hammond wants to forget rules that the UK agreed with the EU to ban non-European companies from the satellites
Instapaper to 'go dark' in Europe until it can work out GDPR compliance