His appointment marks a break with the recent past which has seen Tory peers chosen as the last two heads of the UK's press regulator.
Moses, who has been in the Court of Appeal since 2005, and was due to retire in May, is to take up the £150,000-a-year position immediately and will join the selection panel to appoint IPSO's 12-person board.
IPSO is due to come into operation, replacing the Press Complaints Commission as industry regulator, in June.
Chairman of the selection panel Sir Hayden Phillips said: "Sir Alan's qualities meet all of the criteria my panel judged were most relevant in appointing a chair. He is person of experience and integrity, of independence and vigour, and also personable, approachable, and always open to consider new ideas.
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"With his reputation for being quick, forthright and fearless I believe that not only is he someone on whom the public can depend to tackle abuses by newspapers where they occur, (using the considerable new powers that will be vested in IPSO), but someone who also believes firmly in independent self-regulation of the press and in the vital democratic role of a free press in a free society.
Moses said: "The public and the press are entitled to a successful system of independent regulation. I recognise it is a big responsibility to achieve this.
"I believe that such a system should be designed to protect the public against a repetition of the breakdown in standards in some parts of the newspaper industry in recent times. At the same time it should affirm and encourage the vital role of a free and fearless press.
"I shall do my best to guide the development of clear, simple but fair rules in an area where there are difficult questions and there are no easy answers.
"But I am determined that there should be no hesitation in dealing with bad practice by newspapers and providing support and vindication for those who suffer as a result of any future breakdown.
"This new organisation will have to listen to and learn from the press and their critics in the period ahead.
"To those who have voiced doubts as to the ability of IPSO to meet the demands of independent regulation, I say that I have spent over 40 years pursuing the profession of barrister and judge whose hallmarks are independent action and independent judgment. I do not intend to do away with that independence now."
Moses was born in 1945 and privately educated at Bryanston School and University College, Oxford, and called to the Bar by the Middle Temple in 1968.
From 1981 to 1990 he was a member of the Attorney-General's Panel of Junior Counsel to the Crown, Common Law, and from 1985 to 1990 was Junior Counsel to the Inland Revenue.
He became a QC in 1990 and served as a Judge of the Queen's Bench Division from 1996 until 2005, when he joined the Court of Appeal. He was also Presiding Judge of the South Eastern Circuit from 1999 to 2002.
He is also chairman of Spitalfields Music, a charity which provides two festivals a year and music education for pupils and those of all ages in Tower Hamlets, and was an external member of the Council of the Royal Academy of Arts for six years.
Pressure group Hacked Off remains unimpressed with IPSO.
A spokesman said: "The appointment of Sir Alan Moses as chair of IPSO changes nothing when the structure and operation of this
“Son of PCC” remain so fatally flawed. The real power continues to be exerted by the big newspaper companies that have a veto over budgets, appointments, the Code, investigations, sanctions or any arbitration scheme.
“IPSO – created with no public consultation whatsoever – is clearly designed to defy the recommendations of the Leveson Inquiry on independence, the wishes of all Parliamentary parties and the views of the overwhelming majority of the public. It is a dreadful insult to victims of press abuses, leaving in charge the same shadowy newspaper paymasters who called the shots at the discredited Press Complaints Commission during its worst years and even now.
“External analysis has found that IPSO falls far short of the kind of change Leveson said was necessary, satisfying only 12 out of his 38 specific recommendations. This means that – just like the PCC – IPSO will deny the public fair treatment and will put the interests of editors and proprietors first.
“The best thing Sir Alan Moses could do now is to advise the big newspaper companies to redesign IPSO so that it can meet the basic standards of independence and effectiveness set out in the Leveson Royal Charter. That would give the public the protection from abuses that we know it needs while safeguarding freedom of expression.”
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