Terms have been agreed on a pre-contract arrangement for the 26-year-old midfielder to move to Easter Road next season.
Craig has made over 150 appearances for St Johnstone since signing from Falkirk in 2008.
His five-year deal expires at the end of this season, and he will link up with Pat Fenlon's squad in the summer.
Hibs also declared that they had not breached any SPL regulations in their pursuit of Craig.
A statement on the Hibs website read: "The Club followed the SPL Rules which govern the ability of clubs to approach players registered with other clubs in certain circumstances and St Johnstone had previously been made aware of the pre-contract agreement."