The Switzerland Under-19s international has agreed a four-year deal at the Scottish champions, having failed to break into the first-team at Old Trafford.
The 19-year-old right-back, who joined the Red Devils for £580,000 from Zurich in 2013, managed just one senior appearance.
Janko spent the first-half of last season out on loan at Championship outfit Bolton, where he made 10 outings out of a possible 18.
A club statement read: "Celtic Football Club can confirm that it has completed the signing of Saidy Janko from Manchester United on a four year contract."
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