Shakespeare was undergoing treatment for cancer back in October 2023.
He also worked for West Brom, Hull, Everton, Watford, Aston Villa and Norwich and had a spell as England assistant boss in 2016.
A statement released on behalf of his family via the League Managers’ Association said Shakespeare “passed away peacefully at home surrounded by his family”.
It added: “While the family are immensely proud of his footballing achievements as both a player and a coach, to us, his family, he will always primarily be a loving and loved husband, father, son, brother and uncle.
“The loss is devastating to us all and we would ask that privacy be given at this incredibly difficult time as we try to come to terms with, and mourn, the loss of a very special person.
“The family would like to thank and acknowledge the many prayers and good wishes sent during the past few difficult months, many of which we were unable to respond to but all meant a lot to Craig and the family.”
Shakespeare was Claudio Ranieri’s assistant in 2015-16 when Leicester created one of football’s all-time greatest stories to win the Premier League.
He replaced Ranieri as manager in February 2017 but, having been appointed permanently later in June on a three-year contract, was sacked in October.
Shakespeare’s most recent role was another spell as Foxes assistant in April 2023 under Dean Smith, but he left after their relegation from the Premier League the following month.
During his playing career as a midfielder, he featured for Walsall, Sheffield Wednesday, West Brom, Grimsby, Scunthorpe, Telford and Hednesford.
Former Leicester boss Nigel Pearson, who worked with Shakespeare at five different clubs, said: “It’s difficult to put into words how I, and indeed everyone who came across or worked with Craig, will feel on hearing such devastating news.
“He is without hesitation one of the most wonderfully talented, emotionally understanding, calm, balanced and outrageously funny people I’ve had the privilege of calling my friend. Safe journey to the next destination my wonderful friend.
“You are loved and admired by us all, and every time we think of you, a smile, smirk, chuckle or memorable occasion will come to us. We truly are the lucky ones for having known Shakey.”
Shakespeare was England assistant boss for Sam Allardyce’s one game in charge, a 1-0 win in Slovakia in September 2016.
A social media message from the England national team account read: “We are devastated to learn that former Three Lions coach Craig Shakespeare has passed away at the age of 60.
“All of our thoughts are with Craig’s family and friends at this time.”
A Foxes statement said Shakespeare “leaves a legacy at Leicester City like few others”.
It added: “Though we mourn his loss, we are grateful to have shared such a special connection with a man whose passion and spirit will long resonate with all who had the pleasure of knowing him.
“Craig was not merely a staff member but a cherished part of the Leicester City family. His warmth, kindness, and genuine interest in people endeared him to all.
“His loss will be felt deeply by the many friends he still has at Leicester City and beyond. Supporters, colleagues, and friends won’t ever forget the immeasurable impact Craig had on the football club and its staff.”