The England-born Greece international spent seven years with the Blades before joining Panathinaikos in the summer.
Reports from Greece claim that Baldock was found dead in the swimming pool of his house in Glyfada, southern Athens.
The defender, who was not named in the Greece squad to face England in the UEFA Nations League on Thursday, played for Panathinaikos in Sunday's 0-0 draw with Olympiacos.
A statement from Super League Greece read: "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."
Sheffield United have expressed in their statement that they are "shocked and extremely saddened" to learn of Baldock's passing.
The Blades added: "The defender left the club in the summer after seven years at Bramall Lane and was extremely popular with supporters, staff and teammates who pulled on a red and white shirt alongside him.
"The sincere condolences of everyone associated with Sheffield United are extended to George's family and friends."
A statement from MK Dons, where Baldock began his professional career, read: "We are deeply devastated and saddened to learn about the shocking news of former Academy graduate and MK Dons player, George Baldock.
"George started his career at Stadium MK, where he worked his way through the youth ranks and made his senior career debut at the club before reaching the heights of the Premier League in later years.
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."
Panathinaikos are yet to release a statement of their own, at the time of writing, but the club's official account on X have changed their profile image to an all-back club crest.
According to journalist Fabrizio Romano, the Greek Football Federation have requested UEFA to allow players to wear black armbands in their next two matches against England and the Republic of Ireland in memory of Baldock.
Baldock was born in Buckingham, England and began his career with MK Dons, where he spent eight years between 2009 and 2017 and made 125 first-team appearances.
The full-back, who played alongside his brother Sam Baldock, also experienced loan spell at Northampton Town, Tamworth, Icelandic club IBV and Oxford United before joining Sheffield United on a permanent deal in 2017.
Baldock played 219 times for the Blades across all competitions and was part of the side that secured automatic promotion from the Championship in 2018-19.
Eighty-three of Baldock's 219 appearances for Sheffield United took place in the Premier League, including all 38 outings in the 2019-20 season when the South Yorkshire club secured an impressive ninth-placed finish in the top flight.
Baldock left Bramall Lane upon the expiration of his contract in the summer and went on to make four senior appearances for Greek side Panathinaikos at the start of this season.
He also earned 12 international caps for Greece, earning his first call up under former manager Gus Poyet in May 2022, and qualified to represent the Blue and Whites through his grandmother.