Gordon Brown has completed his Cabinet reshuffle on his first full day as Prime Minister, appointing the UK's first female Home Secretary.There was none of the usual trooping up and down Downing Street for incoming and outgoing ministers as the new PM left No 10 to work at his office in the Commons.Jacqui Smith takes over from John Reid at the Home Office while David Miliband becomes Foreign Secretary, replacing Margaret Beckett, and Alistair Darling was named as Chancellor of the Exchequer.Meanwhile, Jack Straw - Mr Brown's campaign manager - takes over at the Ministry of Justice replacing Tony Blair's ally Lord Falconer.At 41, the former Environment Secretary will become the youngest minister to take the role since David Owen in 1977. His brother Ed Miliband is Minister for the Cabinet Office and will also hold the post of Chancellor of the Duchy of Lancaster.Mr Miliband said he is "tremendously honoured" to become Foreign Secretary and said he wants to bring leadership to the Foreign Office which is "patient as well as purposeful".Douglas Alexander was named as International Development Secretary, ousting deputy leadership candidate Hilary Benn, while Alan Johnson is the new Health Secretary, switching from education.On his own website, James Purnell, MP for Stalybridge and Hyde, confirmed his appointment as Culture Secretary while Peter Hain is the new Work and Pensions Secretary as Hilary Benn is switched to Environment replacing Mr Miliband.The Department of Trade and Industry will be renamed the Department for Business and Enterprise and will be headed by John Hutton who is moving from work and pensions.Ed Balls, Mr Brown's right hand man at the Treasury, has been given the new post of Minister for Children and Schools while Hazel Blears takes over as Communities Secretary from Ruth Kelly who has been given Transport.Des Browne remains as Secretary of State for Defence and is also Secretary of State for Scotland while Baroness Scotland is the new Attorney General replacing Lord Goldsmith.Geoff Hoon is the Chief Whip while Yvette Cooper heads up Housing. The new Northern Ireland Secretary is Shaun Woodward while Baroness Ashton is the Leader of the House of Lords.Andy Burnham is Chief Secretary to the Treasury and John Denham becomes Secretary of State for Innovation, Universities and Skills.The full list can be viewed on Downing Street's website - www.number-10.gov.uk/output/Page12165.asp.The reshuffle saw the resignation of Health Secretary Patricia Hewitt for "personal reasons". In a letter to Mr Brown she said she had decided to step down from Government so she could give more time to her "constituency and family".Although Mr Brown had offered to keep her in the Cabinet she felt it was the "right moment" to go.Harriet Harman won the deputy Labour leadership campaign by a narrow margin on Sunday and has been appointed to the chairmanship of the Labour Party by Mr Brown.Mr Brown promised "a new government with new priorities" in an emotional speech outside No 10 on Wednesday and said he would live up to his old school motto: "I will try my utmost."He acknowledged he must meet a demand for change from an electorate growing tired with ten years of Labour Party rule. Top of his list are changes in schools and in the NHS.The Prime Minister has hired The Apprentice tycoon Sir Alan Sugar to advise him on business. The Amstrad boss will sit on a special Business Leaders Council alongside other industry figures.Mr Brown's final act as Chancellor was to appoint his predecessor Tony Blair to the office of stewardship of the Chiltern Hundreds - meaning the ex-premier is standing down as MP for Sedgefield.A by-election to replace Mr Blair as MP for the Co Durham constituency is expected to be held on July 19, Labour has said. Additionally, another by-election will be held on the same day in Ealing Southall to replace Labour's Piara Khabra, who died last week.© Independent Television News Limited 2007. All rights reserved.