The 26-year-old spent two seasons with Alaves, making 77 appearances in total and 31 in La Liga last season.
Bachmann has joined Watford on a three-year deal after his contract at Stoke City expired, bringing an end to his six seasons at the club.
The 22-year-old has been called up for Austria's senior squad in each of the last two international breaks.
Everton midfielder Tom Cleverley's permanent move to Watford also comes into effect on Saturday. Cleverley joined Watford on loan in January, but Watford opted to make the move permanent in March, handing the 27-year-old a five-year contract.
(Reporting by Simon Jennings in Bengaluru)
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