Baxter had signed a contract until 2023 with an option to have it renewed for a further two years, but Chiefs will now begin their search for a replacement.
The Englishman returned to Naturena for a second spell after a successful spell between 2012 and 2015 during which he won two league titles and two domestic cups.
He resigned with a year to go on his contract.
Chiefs are currently fourth on the DSTV Premiership log, but 18 points behind log leaders Mamelodi Sundowns.
Earlier in the week, Baxter said he is ready to leave his post if the club demands it.
This came after his troops were defeated 1-0 by SuperSport United in a DStv Premier League match last weekend.
Baxter reacted to calls for his resignation.
“I don’t have any message to the fans, because if they want me to go, I will go. If the chairman says to me ‘Stuart, I don’t think you are doing a good job,’ then I will walk.”