The 35-year-old Middlesex and England opening batsman who led England to two Ashes victories and to the top of the Test rankings is retiring after 14 years in the professional game.
He won 100 Test caps, 124 ODI caps and four T20 caps in an international career that spanned 11 years. He scored 21 Test centuries and six ODI centuries.
His captaincy record of 24 wins from 50 matches makes him England's third most experienced leader and the second most successful behind Michael Vaughan.
But the recent 2-0 series defeat to South Africa meant England lost their number one Test ranking to the tourists.
Strauss said: “After much thought over the last few weeks, I have decided to step down as England Test Captain and announce my retirement from all forms of cricket. It has clearly been a tough decision to make, but I believe that it is both in the best interests of the England cricket team and myself to step down at this stage.
“There are too many people who have helped me on this incredible journey to mention them all by name, but I would like to thank all the Middlesex and England players I have played alongside, as well as the phenomenal coaches and support staff with whom I have been fortunate enough to work. Particular mention has to go to Andy Flower and Duncan Fletcher in that regard. It would also be remiss of me not to thank Middlesex County Cricket Club, the ECB and the PCA for their support and guidance over the years.
“No one can play international cricket for any length of time without having an incredibly strong support network around them, and I would like to take this opportunity to thank my family for going through it all alongside me over the course of my England career.
“I am extremely proud of everything I have achieved as a cricketer, and I have found myself very fortunate to play in an era when some of English cricket's greatest moments have occurred. I have loved every minute of it. All that remains is for me to wish Andy, Alastair and the rest of the team the very best for the coming months. I will be an interested spectator.”
Strauss made his England debut in a one-day international against Sri Lanka in 2003 and was awarded his Test cap a year later in 2004 against New Zealand scoring a century on debut.
Strauss will be replaced as Test captain by Cook who will also continue to lead the one-day side.
Cook said: “Andrew’s contribution to England cricket in recent years is evident to everyone who follows the sport but only those of us who have been lucky enough to share a dressing room with him are fully aware of his immense contribution to our success. He has been a fantastic captain, has led from the front for three and a half years and is a true ambassador for the game. To have played 100 Tests for your country is a phenomenal achievement and I want to congratulate him on a superb career. I know this can’t have been an easy decision for him and everyone in the dressing room will be sad to see him go.
“I’m very excited by this new challenge, it is a huge honour to be appointed Test captain and am very much looking forward to captaining the side in India this winter and beyond but my immediate focus is on this current NatWest one day series. Once the series is over I will turn my attention to the Test captaincy and building on the work Andrew has started.”