Ashkenazi held talks with US Secretary of State Mike Pompeo in Jerusalem ahead of his "appointment as minister of foreign affairs this coming Thursday," said Blue and White, which is led by the incoming alternate prime minister, Benny Gantz.
A unity government agreed between Gantz and veteran right-wing Prime Minister Benjamin Netanyahu is due to be sworn in on Thursday evening, ending more than a year of political deadlock.
Foreign affairs was a key profile secured by Blue and White in coalition talks with Netanyahu's Likud party, along with the defence ministry which will be led by Gantz.
Comment: The Netanyahu-Gantz coalition farce
Ashkenazi joined Israel's army in 1972 and fought in the Yom Kippur war a year later.
He also took part in Operation Entebbe, an Israeli commando raid to rescue hostages from a plane that had hijacked by Palestinian and German militants and diverted to Uganda's main airport.
Netanyahu's brother Yonatan was killed in the operation.
Ashkenazi went on to take part in or lead a series of notorious military operations.
Turkey put Ashkenazi and three other Israeli military leaders on trial in absentia in 2012 over the deadly 2010 storming of a Turkish ship that had been bound for Gaza.
He was army chief during Israel's war with Hamas in Gaza in 2008-2009, also known as Operation Cast Lead, in which an estimated 926 Palestinian civilians were killed.
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