Barton, who was released by Newcastle United in the close-season, signed a four-year deal with the west London outfit who were promoted to the top flight as second tier champions last season.
"It's been quite a whirlwind, so to get things finally sorted and draw a line under it all is a great relief," Barton said on the club website.
"The ambition of the club really impressed me.
"The gaffer is talking about adding two or three more bodies and that, combined with the potential of the club and the new owners' ambitions, bodes really well for the future."
Barton, who won his first and only England cap in 2007, is no stranger to controversy and was jailed for assault in 2008 while at Newcastle.
The 28-year-old was also given a suspended four-month sentence for attacking team mate Ousmane Dabo in 2007 during a spell at Manchester City.
"He's coming here to show people what he can do. He wants to get back into the England team," QPR manager Neil Warnock said on the club website.
"He's very enthusiastic. People will say one or two things about him, but they've said stuff about me in the past too, so I won't worry about that."
Fernandes, who is also owner of the Team Lotus Formula One outfit and AirAsia airline, completed his QPR takeover last week and promised to take the club to new heights.
QPR have been linked in the British media with moves for Manchester City winger Shaun Wright-Phillips and West Ham United midfielder Scott Parker.
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