Green-Eyed Monster

This is a phrase commonly known to mean “jealously,” but I’m having trouble figuring out why it means this.

Shakespeare used the phrase at least twice.

In Othello:

O beware, my lord, of jealousy;
It is the green-eyed monster which doth mock the meat it feeds on.

In The Merchant of Venice:

How all the other passions fleet to air,
As doubtful thoughts, and rash-embraced despair,
And shuddering fear, and green-eyed jealousy!

That dates it to the late 1500s. But there’s no reasoning why Shakespeare used it. Did he just make it up?

Another definition noted:

From the association of envy with the color green.

But then where did that association come from?

I found this:

Some believe the color green has been associated with jealousy dating back to the ancient Greeks. They believed jealousy occurred as result of the overproduction of bile, which turned human skin slightly green.

I checked in with a friend who is a (literal) Shakespeare expert. He concurred that the phrase existed long before Shakespeare’s usage, and he had heard the same origin story about the relationship to the color green.