The 28-year-old Frenchman joined Manchester United from Bordeaux in 2009 on a four-year deal, but played just 14 Premier League matches for the club before moving to Newcastle in August 2011.
He made 77 appearances for Newcastle but his time at the club was hampered by thigh and hamstring injuries, and in May 2016 he was let go.
Since then Obertan has had brief spells at Russian side Anzhi Makhachkala and Wigan Athletic before becoming Levski's 11th new signing of the close season, two of whom - Obertan and midfielder Jordi Gomez - are former Wigan players.
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Levski finished third in the league last season.
(Reporting by Angel Krasimirov; edited by Julian Shea)
