The 33-year-old Essex left-hander has amassed 12,254 runs at 44.88 including 32 hundreds, while his run of 158 consecutive Test appearances is a world record.
"After much thought and deliberation over the last few months I have decided to announce my retirement from international cricket at the end of this Test series against India," said Cook in an England and Wales Cricket Board statement.
"Although it is a sad day, I can do so with a big smile on my face knowing I have given everything and there is nothing left in the tank," the four-time Ashes-winner added.
"I have achieved more than I could have ever imagined and feel very privileged to have played for such a long time alongside some of the greats of the English game. "
Cook said it would be tough to walk away but that the timing was right.
"I have loved cricket my whole life, from playing in the garden as a child, and will never underestimate how special it is to pull on an England shirt," he said.
"So I know it is the right time to give the next generation of young cricketers their turn to entertain us and feel the immense pride that comes with representing your country."
England took an unassailable 3-1 lead in their five-match series against India with a 60-run win in the fourth Test at Southampton on Sunday.
But Cook, who scored a century on Test debut against India at Nagpur in 2006, has managed just 109 runs from his seven innings in the series at 15.57.
'Sounding board' Gooch
He is sixth in the all-time list of leading Test run-scorers, having surpassed mentor Graham Gooch's previous England record of 8,900 runs three years ago.
Gooch was also a predecessor of Cook's as an Essex and England opener, as well as Test skipper.
"There are too many people to thank individually, but a special mention must go to Graham Gooch," said Cook, who is to continue playing for Essex.
"As a seven-year-old I queued for his autograph outside Essex County Cricket Club and years later was so fortunate to have him mentoring me," he said.
"Graham was my sounding board, especially in the early years of my career, spending hour after hour throwing balls at me with his dog stick. He made me realise you always need to keep improving whatever you are trying to achieve."
Former England captain Nasser Hussain described Cook -- about to become a father for the third time -- as a "truly remarkable cricketer".
Speaking to Sky Sports he said: "To carry on this long... You'd think somewhere along the line you'd lose form or fitness. Huge credit to the lad. He's been England's best player."
Alec Stewart, another former England skipper, paid tribute to his robustness, telling BBC radio: "That record of over 12,000 runs, if someone breaks it they're very, very good players, but it will take a long, long time to get there."
England have yet to announce their squad for the fifth Test at The Oval, which starts on Friday, but it would be a major surprise if Cook were omitted.