Krikorian's Sling Media - which was sold to EchoStar Communications in 2007 - made the "Slingbox" for watching TV on computers.
Krikorian will join Microsoft with a small team, according to the Wall Street Journal, which reported the acquisition earlier on Wednesday. Microsoft also purchased some patents owned by the start-up related to controlling electronic devices, the newspaper added.
Krikorian and a Microsoft spokesman declined to comment.
Krikorian resigned from Amazon.com Inc's board in late December after about a year and a half as a director at the company, the Internet's largest retailer.