The French winger, 22, has signed for Newcastle on a five-year deal reported to be worth £3m.
"It wasn't really a difficult decision to come here," Obertan told the club's official website. "I spent two good years in Manchester but it was a bit difficult with the competition and I really needed a club where I could play more games.
"I know it won't be easy to play each game here, because there's a good group, but I want a fresh start in my football."
Magpies manager Alan Pardew paid tribute to Obertan's "great pace and excellent technique", adding: "I contacted Sir Alex about him early at the start of the summer to see if there was an opportunity to bring him to Newcastle, but it wasn't until Wayne Routledge joined Swansea that we were able to bring him in.
"His best years are ahead of him, which is exactly what we want at this club, and with the backing of our magnificent fans I'm sure he will prove an excellent signing for us."
Newcastle begin their Premier League campaign with a home fixture against Arsenal on Saturday.