Vice President Joe Biden presided as Schatz, a Democrat, took the oath of office Thursday afternoon at the Capitol in Washington.
Schatz, at 40 one of the younger members of the upper house, will become Hawaii's senior senator when the 113th Congress gets underway next week, Politico reported. Sen. Daniel Akaka, a Democrat, is retiring next month at the end of his current term and will be succeeded by Rep. Mazie Hirono, also a Democrat.
Inouye died Dec. 17 at age 88.
After Gov. Neil Abercrombie announced Schatz's appointment, the new senator flew to Washington with President Barack Obama and his family on Air Force One. Schatz's family, however, had to fly commercial.
Reporters who greeted Schatz at the airport asked him how he liked the presidential plane. He said it was a "lovely flight" and he slept for most of the journey from Honolulu to Washington.
Asked for an outsider view on the budget debacle, the so-called fiscal cliff, he said it was "difficult to understand why we would inflict this on ourselves," so he is "hoping that cooler heads will prevail."
"Everyone seems to agree that we want to avoid this," he said. "There are some practical balanced approaches that have been set forth. And now it's time, and we're really running out of time, to negotiate a settlement, which I believe no one will be thrilled with. But the only thing worse than a solution to the fiscal cliff would be actually going over it."