The prophet Zechariah writes (13:1):
And it shall come to pass on that day, says the L-rd of hosts, that I will cut off the names of the idols out of the land, and they shall no more be remembered: and also I will cause the prophets and the unclean spirit to pass out of the land.
"Unclean spirit"- this refers to the evil inclination (Rashi, on this verse).
See also what the Malbim writes there:
I have already explained in my commentary on Ezekiel that this is a metaphoric representation of the spreading forth of the waters of knowledge and the stream of Torah and faith, which are compared to water. After the first war, the waters of knowledge will begin to spread out from the house of David and the inhabitants of Jerusalem and remove the sin of external consciousness and to purify the impurity of foolishness, stupidity and false belief and every trace of idolatry as is explained shortly. “It will come to pass on that day that I will cut off all the names of the idols from the land…” (Zechariah 13:2) This is an explanation of the nature of this source and its faithful waters that flow from the upwelling of wisdom and holy consciousness. After the final war of Gog and Magog the waters will spread outwards and “the earth will be full of the knowledge of the Lord, as the waters cover the sea.” (Isaiah 11:9) On this it says “And on that day living waters will go out from Jerusalem…and the Lord shall be king over all the earth…” (Zechariah 14:8-9) This is the meaning of the ‘water,’ that everyone will recognize the unity of the Creator and the truth of divinity. This itself is the water which Ezekiel saw, as I explained there.
In this question-answer article, Chabad of New Jersey cites the Rambam, who says, that when Moshiach comes, our sole business will be to "know G-d" (Mishneh Torah; Laws of Kings and Wars 12:5):
.And at that time there won't be any famine or war there, and there won't be jealousy or competitions, for good will be flowing freely, and all delights will be as common as dust, and the only business will be to know G-d. Therefore, Israel will be great sages and they will know the hidden things and they will attain knowledge of their creator as much as people can, as it is said, "For the earth will be filled with knowledge of G-d like water covers the oceans. ...
The article then goes on to explain what Rashi meant with the referal to the evil inclination, and that the prophet Zechariah says that "on that day", the unclean spirit, e.g. the evil inclination will be removed. It means that our choices will not longer include anything bad:
Maimonides writes that when Moshiach comes, our sole occupation will be to know G-d. Since G-d is infinite, we will have unlimited opportunities to expand our understanding of Him. We will have the choice to know G-d through studying holy texts, through delving into the mysteries of creation, or appreciating the beauty around us. We will be able to express our relationship with Him in myriad ways - through art, music, poetry, or through intellectual growth and advancement. As mentioned, our choices will not include anything negative or harmful; yet we will be faced with endless possibilities for personal growth and awareness of the Divine.
So, yes, we will still have a free choice. However, whatever we chose, it will be good, since there will be no evil inclination anymore. One will serve G-d with music, the other with learning Torah all day.
For further reading, see Chapter 11: Mitzvos After the Resurrection by Rabbi Nissan Dovid Dubov.