General Moeen U. Ahmed, the army chief and Muhammad Yunus, the Nobel Peace Prize winner, joined some 1,000 foreign diplomats, government officials and members of parliament at the ceremony.
Campaigning and voting for the elections was generally peaceful, in marked contrast to the unrest that caused polls to be cancelled in 2007, when at least 35 people died in violence over allegations of vote rigging.
The Awami League front won 230 seats out of a possible 300, giving her a clear majority to govern without forming a coalition.
However the new prime minister, who also ruled between 1996 and 2001, has indicated she wants to end the confrontational politics that has paralysed Bangladeshi politics for decades.
"I feel in the parliamentary system we can work together. I am ready to work with everyone," she said following her victory.
Both Hasina and her bitter rival Khaleda Zia, who is also an ex-premier and leads the Bangladesh Nationalist Party (BNP), were jailed for a year by the outgoing army-backed government on corruption charges.
After initially rejecting the election results, Zia said she would work with Sheikh Hasina -- though she stood by allegations of voter fraud and snubbed Tuesday's ceremony.