She replaces Tanzania's ex-ambassador to Britain, Peter Kallaghe, who has returned to the country.
"Dr Migiro will be sworn in (today) ... at the Chamwino state lodge in Dodoma," the president's office said in a terse statement.
The 59-year-old Migiro became Tanzania's first female foreign affairs minister in January 2006 under former president Jakaya Kikwete's government.
She was appointed deputy secretary general of the United Nations a year later and served in that position until June 2012.
After serving at the UN headquarters in New York, Migiro returned home and was appointed cabinet minister until the final years of the Kikwete administration.
She entered the race to become the ruling Chama Cha Mapinduzi's (CCM) presidential candidate in the 2015 general election, but lost the nomination to the eventual winner Magufuli after being shortlisted.