Rangnick will still carry on with his advisory role with Manchester United as planned at the end of this season.
“I’m really looking forward to playing my part in helping United become a real force again,” he stated.
The German has signed a two-year agreement with Austria and will unite with them following the Premier League season ends in May.
“It is an honour for me to take on the role of manager,” he stated.
“The prospect of contesting the European Championships in Germany with a young team hungry for success fills me with great anticipation.”
Austria, who stands at 23rd in the FIFA rankings, have been without a head coach since the departure of Franco Foda in March after their failure to qualify for this year’s World Cup.
“We are very pleased that we were able to win an outstanding expert in international football as team boss,” stated Gerhard Milletich, president of the Austrian Football Association.
“We are all convinced that he is the ideal man and that his vision will advance the national team.”
Red Devils have triumphed 10 of their 25 matches in all tournaments since Rangnick took place of the dismissed Ole Gunnar Solskjaer in November.
Man Utd are 6th in the table, five points behind fourth-placed Arsenal with 3 games to spare.
Ajax manager Erik ten Hag will take over in the summer, becoming Manchester United’s 5th permanent manager since Sir Alex Ferguson’s retirement in 2013.