The social media accounts of Panathinaikos and the Greece national team blackened their profile pictures on Wednesday evening.
Manchester United defender Harry Maguire, who started his career at Sheffield United, posted a picture of Baldock with a broken heart emoji and the letters RIP.
Former Sheffield United team-mate Dean Henderson posted “RIP Blades legend” on X along with a picture of the pair.
The Football Association said in a statement: “We are devastated to learn of the passing of George Baldock at the age of 31.
“Our thoughts and deepest condolences are with George’s family, friends and team-mates at club and country.”
The England national team said on X: “We’re extremely saddened by the passing of George Baldock. George was close to many of our players, and represented Greece – our opponents on Thursday night.
“We’re thinking of George’s family, friends and team-mates at club and country at this difficult time.”
The English Football League said in a statement: “The EFL is deeply saddened to learn of the passing of George Baldock, a player who made a lasting impact with spells across the league at Sheffield United, Oxford United, Northampton Town and MK Dons.
“Our thoughts are with his family, friends and former colleagues.”
Baldock came through the youth system at MK Dons – as did his brother Sam – and the club said: “We are deeply devastated and saddened to learn about the shocking news of former Academy graduate and MK Dons player, George Baldock.
“Everyone affiliated with MK Dons shares a great love for George, Sam and the Baldock family, and we would like to share our sincerest condolences during these awful times. You will always be one of our own, George.”
Northampton Town posted: “We are deeply saddened to learn of the passing of former loanee George Baldock at the tragically young age of 31. Sending our sincerest condolences to George’s family and friends.”
Oxford United, where Baldock’s brother James is club doctor, said: “Oxford United is deeply saddened to learn of the passing of former player, George Baldock, aged 31.
“The sincere condolences of everyone associated with the club are extended to James, Sam, his family, and friends.”
Tamworth, where Baldock also had a loan spell at early in his career, described him as “a brilliant character and a brilliant person”, adding: “George went on to fulfill his potential and will always be remembered by everyone associated with Tamworth Football Club.”
The Greek Super League said: “The entire Super League football family expresses its deep sorrow for the untimely loss of Panathinaikos and our national team footballer, George Baldock, and extends its deepest condolences to his family and loved ones.”