During the Blades' 2019-20 Premier League season the wing-back spoke more than once about discussions with the Greek footballing authorities about taking advantage of his heritage to represent them at international level.
“It is a real honour to represent Greece through my late grandmother, this is a proud moment, not just for me, but for my entire family," said Baldock. "It has been a possibility for a while, so I’m happy now to be in a position where I am available to play. it is an exciting time ahead.”
Former Chelsea midfielder Gustavo Poyet named the Buckinghamshire-born 29-year-old in his Nations League squad.
Greece play Northern Ireland on June 2, and have home and away games against Kosovo either side of a match at home to Cyprus.
The 2004 European champions have not qualified for this winter's World Cup in Qatar.