How and when it was decided that the electron should have negative charge, and protons have positive charge?

that was determined about 6000 and change years ago

Genesis 1:1 in the beginning GOD created the heavens and the earth.

Thats about when HE decided to make it that way

but if you want to know when and why MAN started calling it the way he does

then that would be round about the time of the genius known as nikolas tesla. it was determined that the NEG side of the battery LOST electrons and they traveled through the wire and went to the POS side of the batt

since the NEG side lost the electrons they named it the NEG side.

see electrons have this tendency not to stay with thier respective atoms so they minus themselfs

by the way only the first 3 things i said here I know are true for certain the rest is a mix of intelligent BS but it sounds plausible

The existence and charge of electrons was proven by JJ.Thomson in 1897 using the cathode ray experiment.

The existence of protons in atoms was shown by E.Goldstein by producing Anode Rays.

Benjamin Frankin picked positive and negative. He assumed that anything that had an excess of "charge" was positive. It was later discovered that "charge" actually flowed in the opposite direction of the actual particles. Therefore the particles had to have a negative charge.