Redknapp, 69, will take charge of World Cup qualifiers against Bangladesh and Australia later this month.
He will combine his international duties with the advisory role at Derby to which he was appointed this week.
"This is a fantastic step for the national game in Jordan," said Jordan FA president Prince Ali bin al-Hussein.
"Harry is a world class manager with an internationally recognised record at the highest level."
He has also previously managed Bournemouth, West Ham, Portsmouth and Southampton.
Jordan, who have never qualified for a World Cup, are currently second in their group in the second of three phases of Asian qualifying for the 2018 finals in Russia.
They were previously managed by former England midfielder Ray Wilkins between September 2014 and June last year.
Former Tottenham and QPR boss Harry Redknapp has been appointed manager of the Jordan national team for their next two games.