Muller made 69 first-team appearances for Barnsley during his two years with the club.
Meanwhile the Tykes have signed former York City striker Onome Sodje on a one-year contract.
The 20-year-old began his career at Charlton Athletic before moving on to Ebbsfleet United, he joined York in June 2007 and made 81 league appearances, scoring 22 goals.
Davey told the club's website: "Onome is one for the future and a player we are looking forward to working with at Oakwell.
"He is lightening quick with an eye for goal and is someone we feel we can improve and develop."
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