The two clubs have agreed a fee for the 24-year-old, and he will discuss terms with the Edinburgh club on Monday.
Yeovil boss Steve Thompson told the club's website: "Naturally, I am disappointed to lose a player of Lee's ability.
"But the move, if completed, is a fabulous opportunity for Lee to advance his career in Scotland.
"Hearts are currently second in the SPL and have a tremendous chance of playing in the Champions League, and Lee is very keen to test himself at this high level."