Gooch has been a key figure in guiding his fellow Essex and England opening batsman since the earliest days of the 33-year-old Cook's career.
It was Gooch's mark of 8,900 runs that Cook surpassed three years ago to become England's all-time leading Test run-scorer.
Cook, whose 160 Test appearances also represent an England record, has since broken the 12,000-run barrier to lie sixth in the equivalent worldwide all-time list.
"Alastair has been the rock of England's batting for the last 12 years since he made his debut -- and while we are all sad to see him retire, we must rejoice in what he has done for our country," said Gooch of his fellow former England captain.
"He is a genuine legend of English cricket," added Gooch, now the president of England's Professional Cricketers' Association.
'Perfect role model'
"He is a legend not only because of his performances, but because of his attitude, his sacrifices, the way he has carried himself and the example he has set.
"Alastair is a perfect role model... He is a great ambassador for his sport; he is a great person as well as a great cricketer."
Gooch, 65, said he had long admired Cook's strength of character.
"He has been his own man all the way through. It was evident from the very first time I met him when he came to Essex that he was a smart lad -- and he knew how he could play, he knew how he could manage his game, even at a young age.
"To achieve what he has in playing 160 Test matches, scoring over 12,000 runs and 32 centuries is an incredibly special achievement from a special person."
Cook has indicated he wants to continue his Essex career next season, a move that Gooch welcomed by saying: "For Essex it is a dream come true.
"Knowing Alastair like I do, he will give the same commitment as he did for England."
It was only last week, with Cook averaging a mere 18.62 from nine Tests this year, that Gooch voiced fears about his international future.
"My concern would be watching him that I don't see any improvements in his game," Gooch told BBC Radio Four's Today programme. "He's flatlining a little bit."
But two of Gooch's fellow ex-England captains, Nasser Hussain and Alec Stewart, joined him Monday in congratulating Cook on his career.
"To carry on this long... You'd think somewhere along the line you'd lose form or fitness," Hussain told Sky Sports.
"Huge credit to the lad (Cook). He's been England's best player."
Meanwhile Stewart, speaking to the BBC, hailed Cook's endurance.
"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," he said.
First Published: September 3, 2018, 7:52 PM IST