The Bangladesh Cricket Board made the decision on Tuesday after former South Africa batsman Neil McKenzie relinquished the role earlier this week citing family reasons.
Having featured for the Black Caps for a decade, McMillan had scored over 8,000 international runs in Tests, ODIs and T20s.
After retirement, McMillan worked as New Zealand’s batting and fielding coach from 2014 to 2019.
He also has coaching experiences with Canterbury, Middlesex and Indian Premier League team Kings XI Punjab.
Bangladesh are scheduled to tour Sri Lanka for three Test matches in October-November this year.
McMillan will join the team during its pre-tour camp in Sri Lanka, BCB said in an announcement.