McKillop was born in Dreghorn, a small village in North Ayrshire. He was educated at Irvine Royal Academy and then Glasgow University, where he took a BSc (Hons) and PhD in Chemistry. He joined the ICI Petrochemical & Polymer Laboratory (later renamed the ICI Corporate Laboratory) at Runcorn in 1969 after post-doctoral research work in Paris. He moved to ICI Pharmaceuticals Division in 1975 and, having held a number of positions in Research, in 1989 he was appointed Technical Director of ICI with international responsibilities for research, development and production.
In 1993, ICI Pharmaceuticals demerged to become Zeneca, and in 1994 he was appointed chief executive officer of the new company. In April 1999, Zeneca merged with Astra to form AstraZeneca PLC. McKillop became chief executive officer (CEO) of the merged company. He retired from AstraZeneca on 1 January 2006, when David Brennan took over as AstraZeneca's CEO. McKillop became the chairman of the Royal Bank of Scotland (RBS). His brother, Alexander "Sandy" McKillop, was Professor of Organic Chemistry at the University of East Anglia from 1970–96.
McKillop chaired RBS during the tenure of CEO Fred Goodwin, who promoted aggressive expansion of the bank by acquiring other banks. From the time that Goodwin took over as chief executive until 2007, RBS's assets quadrupled, its cost-to-income ratio improved markedly, and its profits soared. In 2006 pre-tax profits climbed 16% to £9.2 billion with most of the growth coming from its investment banking business. By 2008 RBS was the fifth-largest bank in the world by market capitalisation. One of the factors in its rise was its enthusiasm for supporting leveraged buyouts. In 2008 it lent $9.3bn, more than double its nearest rival.
However, following investor unrest in the build-up to RBS's acquisition of a $1.6bn minority stake in Bank of China in 2005 Goodwin was criticised by some RBS shareholders for putting global expansion ahead of short-term financial returns. Between 2002 and 2005 the share price plateaued at around £17 per share, having nearly trebled between February 2000 and May 2002. Goodwin was accused of megalomania by some shareholders, as reported by Dresdner Kleinwort analyst James Eden (who said he thought the label was 'unwarranted'). After the Bank of China deal, he was forced to promise RBS shareholders he would not indulge in any further big acquisitions and focus instead on growing the group organically.
However, in early 2007, the Dutch bank ABN AMRO was under pressure from hedge funds, including Chris Hohn of the hedge fund TCI, to break itself up to maximise shareholder value. ABN chief executive Rijkman Groenink suspected RBS of acting in concert with the hedge fund Tosca, which was chaired by former RBS chairman Mathewson and recommended the takeover bid of an RBS consortium, against the proposed merger with Barclays Bank. Goodwin arranged a consortium of RBS, Fortis and former RBS shareholders Grupo Santander, to purchase the assets of ABN AMRO and break them up in a three-way split. According to the proposed deal, RBS would take over ABN's Chicago operations, LaSalle Bank, and ABN's wholesale operations; while Santander would take the Brazilian operations and Fortis would take the Dutch operations. In a manoeuvre "labelled in all quarters as a poison pill" ABN AMRO agreed to sell key RBS target LaSalle to Bank of America for $21bn, but in July 2007 the consortium offered the same $98bn for ABN's remaining assets, with a higher cash component (93%).
The deal was struck in October 2007 as the global liquidity crisis began to develop, with Barclays withdrawing its EUR61bn bid and ABN's shareholders endorsing the EUR71bn RBS takeover. Coming after the nationalisation of Northern Rock due to the freezing of the wholesale money markets, the deal proved the final straw for RBS, as it severely weakened its balance sheet not only through the size of the acquisition but due to ABN AMRO's substantial exposure to the US subprime mortgage crisis.
While at RBS, the value of the bank's shares fell below a quarter of their level in early 2007. Following criticism from the press for the takeover of ABN AMRO and the UK government having to bail out the bank, McKillop announced his early retirement as Chairman of the Royal Bank of Scotland on 13 October 2008. At a meeting of the Treasury Select Committee of the House of Commons on 10 February 2009, he admitted to having no qualifications in banking. Like the retired bankers present, he apologised for the financial crisis.
McKillop married Elizabeth Kettle in 1966 and has three children.
- 2002 Knighted in the 2002 Queen's Birthday honour's list for services to the pharmaceuticals industry.
- 2003 Elected Fellow of the Royal Society of Edinburgh 
- June 2004 – awarded an honorary doctor of Sciences by the University of St Andrews
- 2005 Elected Fellow of the Royal Society 
- 2005 Annual Centenary Medal, Society of Chemical Industry
- 2006 Honorary Doctorate from Heriot-Watt University 
- 2007 Royal Medal of the Royal Society of Edinburgh
- Non-executive director of BP, having been a non-executive director of Lloyds TSB Group plc from 1999–2004
- Chairman of the British Pharma Group
- Pro-Chancellor of the University of Leicester
- Vice-President of the European Federation of Pharmaceutical Industries and Associations
- Chairman of the North West Science Council.
- President of the Science Council (January 2007)
- Board of Administration Evolva
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- Marketwatch, 16 July 2007, Timeline of the battle for ABN AMRO
- Farrell, Sean (11 February 2009). "Treasury Select Committee: Bonfire of the bankers – Business Analysis & Features, Business". London: The Independent. Retrieved 3 April 2009.
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- "Fellowship of the Royal Society". Royal Society. Retrieved 4 December 2014.
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- "AstraZeneca". Retrieved 9 August 2005.