Mr Cockburn, interim chief executive at power generation company Aggreko in recent months having been its finance director since May 2000, will take up his new role as group chief financial officer for Serco at the end of October alongside former colleague Rupert Soames.
Although it was widely known Mr Cockburn would be leaving Aggreko at the end of September the business appears to facing a transitional phase before its new chief executive, British Gas boss Chris Weston, joins next year.
Chairman Ken Hanna will assume an executive role until that time with Carole Cran, a long serving financial controller with Mr Cockburn, having already stepped up to become chief financial officer in June.
Mr Cockburn's new annual salary of £500,000 compares to the £400,000 he was paid as finance director at Aggreko, although he was given a £200,000 top up when he took over as interim chief executive in May.
With bonuses and long-term incentives Mr Cockburn, who is thought to have ruled himself out of taking on the Aggreko chief executive role, was paid £1.5m for 2012 and £1.15m for 2013 by Aggreko.
At Serco he will receive a pension allowance of £150,000 with his maximum annual bonus being £650,000. Alongside that he will be eligible for an annual share award worth up to £875,000.
On joining Serco he will receive share options worth up to £675,000, equivalent to 135 per cent of his base salary, dependent on how the business does, On top of that he will get a further set of share options, which are not performance related, and are valued at £240,000.
Serco stated Mr Cockburn will also receive some relocation expenses as he moves from Scotland to be closer to the headquarters of his new employer in Hampshire.
Mr Cockburn, a non-executive director at GKN and former managing director of Pringle, said: "I will be sad to leave Aggreko after fourteen enjoyable and successful years. I am excited to be joining Serco as I have always admired the services it delivers and the passion and commitment of its people.
"I am greatly looking forward to meeting my new colleagues and to working once again with Rupert Soames, with whom I worked for eleven years whilst he served as CEO of Aggreko."
Mr Soames, Serco chief executive, said: "[Angus] was instrumental in the success of Aggreko, is a highly experienced CFO, and he and I have complementary skills."
Serco's chief financial officer Andrew Jenner will step down at the end of September.
Alastair Lyons, chairman of Serco, said: "Angus Cockburn is a highly experienced FTSE100 CFO with a significant track record of success, and he and his team have driven growth in Aggreko by developing customer-focused strategies and consistently delivering against them.
"Angus is a passionate believer in public services and I am absolutely delighted that he has chosen to join Serco and will help lead the company's future development."
The challenge for Mr Cockburn in his new role was laid out by Serco's half-year results which saw currency fluctuations, lost contracts and lower margins contributing to a £7.3 million loss at the outsourcer.
That compared to a £106.1 million profit in the first six months of 2013.
Revenue was down 4.5 per cent to £2.43 billion in the period to June 30 this year but Serco said there would have been a 1.1 per cent rise on a constant currency basis.
The biggest contract win in the period was the 15-year deal to run the Caledonian Sleeper rail services, estimated to be worth around £800m.
But Mr Soames said it had been a poor first half with fewer contract wins than expected but he expects improvement in the second half of the year.
Serco's senior independent director will now be Mike Clasper, with Malcolm Wyman relinquishing the role but continuing to chair the audit committee.
Shares closed up 1.6p or 0.49 per cent, at 330.5p.