The South Asian nation's only Nobel laureate and a harsh critic of Hasina, Yunus, 84, arrived in Dhaka following medical treatment in Paris, after protesters backed him for the role in a government tasked with holding elections for a new leader.
"I feel good coming back home," the economist said at the airport, where he was greeted by top military officers and student leaders.
The student protesters had saved the country and that freedom had to be protected, he said, adding, "Whatever path our students show us, we will move ahead with that."
Yunus is set to be sworn in as chief of a team of advisers at 1430 GMT, at the official residence of President Mohammed Shahabuddin.
Hasina's Awami League party does not figure in the interim government after she resigned on Monday, following weeks of violence that killed about 300 people and injured thousands.
In a Facebook post, her son Sajeeb Wazed Joy said the party had not given up, however, and was ready to hold talks with opponents and the interim government.
"I had said my family will no longer be involved in politics but the way our party leaders and workers are being attacked, we cannot give up," he said on Wednesday.
Yunus, known as the 'banker to the poor', received the 2006 Nobel Peace Prize for founding a bank that pioneered the fight on poverty through small loans to needy borrowers.
Hasina's dramatic exit from the country she ruled for 20 of the last 30 years, winning a fourth straight term in January, triggered jubilation and violence as crowds stormed and ransacked her official residence unopposed.
She is sheltering at an air base near New Delhi, the Indian capital, a development that Yunus said sparked anger at India among some Bangladeshis.
The student-led movement that ousted Hasina grew out of protests against quotas in government jobs that spiralled in July, provoking a violent crackdown that drew global criticism, though the government denied using excessive force.
The protests were fuelled also by harsh economic conditions and political repression in the country, born after a war of liberation from Pakistan in 1971.
