Including the Brock Osweiler trade, Cleveland now owns Houston's first- and second-round picks for next year.
A quintessential leader, Watson propelled the Tigers into the national title game in each of the past two years, splitting with Alabama.
Watson compiled a 67.4 completion rate, a 107.2 passer rating and a 32-3 record while running for 1,934 yards and 26 touchdowns in three college seasons.
Although he was the third quarterback off the board -- behind North Carolina's Mitchell Trubisky and Texas Tech's Patrick Mahomes -- many scouts believe he's the most promising prospect in this year's class.
"You can say he's better than Dak Prescott," one scout told Bob McGinn of the Milwaukee Journal Sentinel. "Total winner. Highly poised. Top intangibles. Lot of predetermined throws. Going to need a lot of work, like all these guys from the spread."
Watson will have to work with O'Brien, however, to improve his mechanics, progressions and high interception totals.