The England-born Greek international was found dead in his swimming pool at his home in Glyfada, south of Athens.
Initial autopsy results suggest he drowned and police sources say there is no evidence of foul play.
His body was discovered at 22:30 local time on Wednesday.
Police tried to resuscitate Baldock at the scene but were unable to do so and an emergency room confirmed his death, Reuters reported, citing a police source.
Baldock moved to Greek club Panathinaikos in the summer after seven years with the Blades.
“We confirm that George has sadly passed away,” the family said in a statement.
“As a family we are shocked by this terrible loss.” Panathinaikos said in a statement: “The Panathinaikos family is mourning his untimely passing.
We support George Baldock’s family and loved ones.” Sheffield United were also shocked by the news, saying: “The defender left the club in the summer after seven years at Bramall Lane and was with the fans, hugely popular.” Next to him were employees and team-mates wearing red and white jerseys.
“Everyone associated with Sheffield United sends their deepest condolences to George’s family and friends.”
Baldock made four appearances for Panathinaikos, including as a starter in Sunday’s goalless draw with Olympiacos.
He made 12 international appearances for Greece, earning a place in the squad thanks to his grandmother.
Greece face England in the Nations League on Thursday but Baldock has not been selected for that match.
The Greek national team said in a statement: “The national team and the Greek Football Association say goodbye to George Baldock with deep sadness and sorrow.”
There are no words to describe the human pain caused by the news of the sudden passing of one of our young people.
The moment is marked by silence.
Our condolences to his family.
Our thoughts and prayers to his second family.”
Baldock began his career with MK Dons in 2009 and played over 100 games for them.
He was loaned out to several clubs, including Northampton and Oxford United, before moving to Sheffield United in 2017.
He made 219 appearances in all competitions for the club and helped them to promotion to the Premier League in 2019 and 2023.
Although Baldock was born in Buckingham, he decided to represent Greece, receiving his first national team call-up by manager Gus Poyet in May 2022.
The following month, he made his international debut against Northern Ireland at Windsor Park in Belfast, in a 1–0 win.