The company confirmed yesterday that Mr Cockburn, who is 52, will join the WH Smith board tomorrow and become chief executive on 1 January when Sir Malcolm Field retires.
He will be paid pounds 425,000 a year for a two-year rolling contract. This will be reduced to one year thereafter. He will also be awarded share options in the company next February, although the number has not yet been decided.
His appointment was immediately criticised in the City where analysts expressed surprise that the company had selected a candidate who has spent his entire working life in the public sector with the Post Office.
Mr Cockburn faces a tough challenge at a company whose profits have been ravaged by tough conditions on the high street and fierce competition from the supermarkets.
One of the attacks Mr Cockburn faces is the challenge from Tesco on the distribution of newspapers and magazines. "I'd like to understand that a bit more," Mr Cockburn said.
Although he declined to make any early statements on strategy he denied that the jump from a state-owned monopoly to a quoted company in the full glare of private competition would prove a problem.
However, City analysts expressed surprise at the company's choice. One said: "This is not a conventional retail appointment. I'd have been happier if it had been someone with a strong retail background but those people are in very short supply at the moment."
Tony Shiret, a long-standing critic of the group said it was a "surprise choice" but added: "I'm not prepared to write him off just because he has come from the Post Office."
Another analyst said: "I'm not convinced that the Post Office is a good training ground for high quality of service and value retailing. It is not enough to change my stance on the group." Institutional investors are also withholding judgement on the appointment: One fund manager described Mr Cockburn as "a bit of an unknown quantity."
Justifying his decision, WH Smith's chairman, Jeremy Hardie, said: "I don't think it matters where he's come from. He's a very good leader, good at managing change." He added that there had been four candidates for the job.
Mr Cockburn has been frustrated by the Government's failure to privatise the Post Office and his departure has been expected.
Commenting on his new role he said: "I'm very excited. My first impression of WH Smith is that you've got a high street name that is deeply embedded in millions of people's minds. It is like the Post Office - in touch with the community every day."
Mr Cockburn's pay is substantially more than the pounds 250,000 he earned at the Post Office. It is also more than the pounds 325,000 received by Sir Malcolm Field last year. WH Smith said the increase was due to a pensions adjustment. Sir Malcolm will receive "modest" compensation for agreeing to stay on past his previously agreed retirement date this August.
The eldest of eight children, Mr Cockburn was born in Edinburgh and raised in a high-rise flat and then a four-bedroom council house. Although he had sufficient qualifications to go to university, he left school at 18 and joined the Post Office. He has been developing his private sector experience recently by accepting non-executive directorships. He joined the board of Lex, the car and truck dealership, three years ago and is also a non-executive director of Whitbread, the brewing and leisure group.