The decision followed a five-hour meeting of Bangladesh President Muhammad Shahabuddin with protesting student leaders, some business elites, civil society members and army chiefs late on Tuesday.
They agreed to appoint Yunus as the head of the caretaker government until the next general elections, IRNA reported citing AFP.
84-year-old Yunus and his bank named "Grameen" won the Nobel Peace Prize in 2006 for his efforts to lift millions of people out of poverty and grant loans to impoverished rural people.
The unrest gripped the South Asian nation early last month after a High court ruling that allowed the government to go ahead with its plan for the job quota system.
The protesters, mostly students took to the streets to denounced the plan that would give more than 50% well-paid civil services jobs to a specific section, including the descendants of those who fought for the country’s freedom from Pakistan in the 1970s.
Some 200 people lost their lives during violent encounters between police and pro-, anti-job quota protesters in Dhaka and other major cities.
76-year-old Sheikh Hasina came to power as prime minister in 2009 and won the elections for the fourth time in the elections last January resigned on Monday and fled the country. She had described the demonstrators as "terrorists". She is currently in India and likely to leave for the United Kingdom.
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