Costas, a Commack native, had worked for HBO since 2001.
In a statement, HBO said: "Bob Costas was a terrific addition when he joined HBO Sports eight years ago, providing us with a distinct and unique presence. Television is about change and we respect Bob's decision to move to the MLB Network. We are very proud of the work Bob did at HBO, and we wish him well in his new endeavor."
Costas' first interview as part of his new job will be with Joe Torre, who has attracted controversy and some criticism for his new book, "The Yankee Years."
The inteview is set to air on Thursday.