Ellison, who co-founded the database company that became Oracle in 1977, will become executive chairman and chief technology officer.
Under the new arrangement, all manufacturing, finance and legal functions of Oracle will report to Catz, while sales and service units will report to Hurd. Software and hardware engineering will continue to report to Ellison.
"While there was some speculation Larry could step down, the timing is a bit of a head scratcher and the Street will have many questions," said Daniel Ives, an analyst at FBR Capital Markets. "Investors have a mixed view of Safra and especially Hurd as co-CEOs given the missteps we have seen from the company over the past few years."
Oracle shares fell 2.4 percent to $40.55 in after-hours trading, after it reported sales below Wall Street's average forecast.