The 18-year-old Swede had five goals and four assists in 26 games with Djurgarden of the Swedish Elite League last season.
Zibanejad added 12 goals and nine assists in 27 games with Djurgarden's junior team.
The six-foot Zibanejad, whose mother is Finnish and father is Iranian, speaks Swedish, Finnish and English.
Ottawa, which had a miserable 2010-11 campaign, is in the middle of a rebuild that saw the club trade away a number of veteran players last season.
The Senators also hold the 21st pick in the draft, which they acquired from Nashville as part of the Mike Fisher trade.