Joe Root is set to be confirmed as England's next captain
Cook brought the curtain down on his four-year tenure during which he became England’s longest serving skipper with 59 Tests at the helm.
But he admitted to Andrew Strauss that he did not have the energy to carry England through two series this summer and an Ashes tour next winter.
Strauss said he did not try to persuade Cook to stay on.
Alastair Cook was England's longest-serving test captain
England's top 10 overseas Test victories
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England headed to Sydney with the 2010-11 Ashes in the bag but a series win was at stake. Hundreds from Alastair Cook, Ian Bell and Matt Prior set up a total of 644 before the seamers forced the tourists to an innings win
“I’ve been there myself. You either know if you have got it in you to carry on, or, deep down, you know it’s time to step aside. And he did it the right way.
“Alastair knew how much drive, determination and energy was going to be required of the England captain in the next 12 months or so.
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Joe Root is set to be named England's 80th test captain
“He had some thoughts and reservations about how much he had left in the tank as England’s longest-serving Test captain, and over the last ten days or so, it was clear his mind was made up.”
Root will be England’s 80th Test skipper and will be unveiled before the one day touring squad, captained by Eoin Morgan, head to the Caribbean for a three-match ODI series with West Indies on February 22.