Southampton fired Welshman Hughes after a 2-2 draw at home to Manchester United last weekend left the south-coast club in the relegation zone with one win from 14 league matches.
Hasenhuttl guided newly-promoted RB Leipzig to second place in the Bundesliga in the 2016-17 season before leaving the club in May this year after a dispute over a new contract.
The 51-year-old ex-Austria forward will be Saints' fourth manager in two years with Claude Puel and Mauricio Pellegrino also being sacked since Ronald Koeman left for Everton in 2016. (Reporting by Nick Mulvenney, editing by Ken Ferris)
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