RAW: The Great Weapon Master feat does not apply to unarmed strikes.
(nor RAI, nor any other acronym I can think of)
The two benefits from the feat occur when:
- when you score a critical hit with a melee weapon or reduce a creature to 0 hit points with one
- Before you make a melee attack with a heavy weapon that you are proficient with
and unarmed strikes are neither of those.
I don't see any ambiguity in this and I'd be reluctant to allow it as a house rule. Scratch that, I wouldn't consider it at all; +10 damage to 3 attacks is a catastrophic increase in efficacy that would catapult the monk into super human early game levels and make it nearly impossible for you to balance any creature used against the party.