Norwich, currently 16th in the 20-team league, did not disclose a fee for the 27-year-old centre-back who has made 39 appearances for the side that finished runners-up to Bayern Munich in the Bundesliga last season.
Klose follows winger Matt Jarvis, Portugal under-21 right back Ivo Pinto and teenage midfielder Ben Godfrey to the Canaries' Carrow Road ground.
"Timm has got plenty of experience having played in the Bundesliga, in the Champions League and for his country," manager Alex Neil told the club website (www.canaries.co.uk).
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"As a player, he's got good technical ability and he's solid in the air."
Switzerland were group runners-up to England in Euro 2016 qualifying.
"When I started football, for me it was always a dream to play in the Premier League and now Norwich have given me a big chance," said Frankfurt-born Klose.
(Reporting by Alan Baldwin, editing by John Stonestreet)
