* James Murdoch returns as chairman of European pay-TV group
* Appointment revives questions about Fox's ambition
* Posts record customer addition, strong profit growth (Adds details, James Murdoch comment)
By Paul Sandle and Kate Holton
LONDON, Jan 29 (Reuters) - James Murdoch is to return as chairman of Sky four years after a phone-hacking scandal forced him out, potentially taking the Murdoch family a step closer to full ownership of the European pay-TV group.
Murdoch, 43, built Sky into a powerhouse in four years as chief executive and five as chairman, and was on the verge of selling it to U.S. media group 21st Century Fox, owned by his father Rupert, before the scandal engulfed him.
His appointment, seven months after becoming chief executive of Fox, follows Rebekah Brooks' return to lead Rupert Murdoch's newspaper business last year after being cleared of charges over the scandal at the News of the World newspaper, where reporters hacked into phones to obtain stories while she was the editor.
Murdoch's return to a top job at Sky had seemed a remote possibility when he stood down from the chairmanship in 2012, but stayed on the board as a non-executive director.
Politicians lined up to denounce the family for its domination of the British media and Prime Minister David Cameron acknowledged that politicians had got too close to his father Rupert.
"It's like Murdoch's getting the band back together, it's as if nothing ever happened at all," said a former executive from Murdoch's British arm.
The admission of phone hacking, including the mobile phone of a murdered schoolgirl, led to a criminal trial, a national inquiry into media standards and a political backlash that forced Fox to abandon its bid for Sky. Rupert Murdoch closed the News of the World in 2011.
In the four years since he stepped down as chairman, Sky bought Fox's German and Italian businesses, rolling the European pay-TV assets into one company with 21 million customers and a London listing. It is 39 percent owned by the U.S. group.
James Murdoch said in 2015 that for Fox, having 40 percent of an unconsolidated asset was not "an end state that is natural for us" but that they had no immediate plans to acquire the rest of the company.
Buying all of Sky, which reported a better-than-expected 12 percent rise in profit and a record number of new customers on Friday, would add Europe's biggest pay-TV group to a media empire that spans U.S. network TV, Asia's Star and one of the most famous production businesses in the world.
Recent results have shown that American TV networks are starting to struggle as viewers shift to online services such as Netflix.
Sky's Chief Executive, Jeremy Darroch, said Murdoch, who was the only candidate put forward, was "without a doubt the right man for the job", underlining his deep knowledge of the international media industry and experience on the board.
Darroch acknowledged there would be speculation about Fox's intentions, but said Sky's management would not be distracted.
"I can't speak for Fox but what I would read into James' acceptance of the role is that he and they continue to be passionate supporters for Sky's ongoing success," he told reporters.
The younger son of the media tycoon quit as the chairman of the-then BSkyB in 2012, brought down by his link to the newspaper business which he was running at the time.
Having returned to New York, he rebuilt his career at Fox. He will replace Nick Ferguson, who has been chairman of Sky since 2012 and on the board for 12 years, at the end of April.
"One of things that's really worked well is we've had continuity at the top of the business," said CEO Darroch. "James in particular has always had very very strong support at the board of the company and from shareholders, and a lot of people recognise his contribution to Sky."
Sky has performed strongly in recent years in its main markets of Britain and Ireland, where its product innovation, slate of programming and marketing prowess have countered the threat from new rival BT.
Shares in Sky were trading up 2.5 percent at 1,067 pence at 0933 GMT, valuing the group's equity at 18.35 billion pounds.
Jeff Li, co-fund manager of the New Capital fund at EFG Asset Management which is a Sky investor, said shareholders were likely to welcome Murdoch's return.
"We think he's demonstrated enough skill over the years in management," he said. "As an investor in 21st Century Fox as well, we always consider it a real possibility for Fox to fully take over Sky at some point."
Another investor, Royal London Asset Management, however described the appointment as inappropriate.
"Should Fox make a bid for Sky, investors need a strong independent chairman to protect the interests of minority shareholders and negotiate the best possible deal," said Ashley Hamilton Claxton, corporate governance manager at RLAM. ($1 = 0.6947 pounds) (Additional reporting by Sinead Cruise, Editing by Timothy Heritage and Anna Willard)