The 57-year-old Petkovic, who helped guide Switzerland to the quarter-final of the European Championship this month, has signed a three-year contract with the French club. "We are so proud to be able to recruit Vladimir," club president Gerard Lopez said in a statement.
The Red Devils have agreed a deal to sign the Real Madrid defender.
British media reported on Monday that United and Real have agreed to an initial fee of 34 million pounds ($47 million) for the 28-year-old, which could rise to 41 million pounds with add-ons. Varane, who had one year left on his Real contract, played more than 350 times for the club, winning three La Liga titles and four Champions League trophies during his time in Spain after joining from French side Lens in 2011. The centre back's addition will strengthen United's defence as Ole Gunnar Solskjaer's team look to challenge for the Premier League title after finishing second last season, 12 points behind champions Manchester City.