If approved, the 67-year-old who retired in 2016 would become the first African-American to lead the Pentagon.
Mr. Biden has been facing calls including from Democratic Asian, Black, and Latino caucuses to nominate minorities to senior cabinet posts.
Veteran Pentagon official Michèle Flournoy, who would have been the first woman to hold the position, had also been considered a front-runner – as well as Jeh Johnson, a former Pentagon general counsel and former secretary of homeland security.
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Four-star Gen Austin served under the Obama administration, leading the US Central Command, whose area of responsibility includes the Middle East, Central Asia, and part of South Asia, between 2013 and 2016. He was the main military architect of the US-led offensive against the Islamic State group in Iraq and Syria.
Before that, he was vice-chief of staff of the Army and the last commanding general of the US forces in Iraq. During these years he worked closely with Mr. Biden, who was vice-president in the Barack Obama administration.
Gen Austin has a reputation for strong leadership and for avoiding the public eye, giving few interviews, and opting to not speak publicly about military operations.