Rangnick has signed a two-year contract and will start work at the end of this season, preparing Austria for upcoming UEFA Nations League games.
Rangnick's contract will be extended until 2026 if Austria, who failed to qualify the 2022 FIFA World Cup in Qatar, makes it to EURO 2024 in Germany.
When Rangnick was hired to replace Ole Gunnar Solskjaer back in November, the plan was to stay on in an interim role until the end of the season before moving into a consultancy role at the Old Trafford club for two years.
The former RB Leipzig manager will still continue in his consultancy role at Manchester United alongside the Austria job.
"We are very pleased that we were able to [appoint] Ralf Rangnick, an outstanding expert in international football, as team boss," said OFB president President Gerhard Milletich.
"We are all convinced that he is the ideal man and that his vision will advance the national team and the OFB."
Rangnick has told United’s official website of the decision to take on two positions: “I will take over as national team manager of Austria at the end of the season but will continue my consultancy with Manchester United.
“I’m really looking forward to playing my part in helping United become a real force again.
“It is an honour for me to take on the role of [Austria] manager.
“The prospect of contesting the European Championships in Germany with a young team hungry for success fills me with great anticipation.”
Rangnick has failed to inspire the needed change at Manchester United, with the club in danger of missing out on Champions League qualification.