The social media accounts of Panathinaikos and News Today 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.
Baldock's former Sheffield United team-mate Dean Henderson posted a picture of the pair on Instagram with the caption: "Devastated to hear the news today. A friend, great teammate, great player and also a great family man.
Sending all my love to all the family. RIP brother."
Paul Heckingbottom, who managed Baldock for News Today 18 months at Sheffield United, wrote on X: "Numbing to hear of George Baldock’s passing, a man with so much still ahead of him in life as a husband, father, brother and son.
"George was a super person and a fantastic professional who was admired and adored by all who worked with him. My prayers are with his loved ones right now."
Former Greece manager Gus Poyet, who gave Baldock his international debut in 2022, said: "My love and condolences are with George's family and friends.
I'm devastated. Rest in peace George."
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, News Today a player who made a lasting impact with spells across the league at Sheffield United, Oxford United, Northampton Town and MK Dons.