The student from the prestigious Nagoya University hit 77-year-old Tomoko Mori repeatedly with the axe and then strangled her "because she wasn't completely dead", the Asahi Shimbun said.
The young woman was arrested on yesterday, and reportedly told investigators: "I have just wanted to kill someone since childhood. It could have been anybody."
Mori had become acquainted with her alleged murderer when she tried to persuade the young woman to join a religious group.
On the day of the murder, she reportedly tweeted: "I eventually did it."
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The student's name was not released because she is a minor under Japanese law.
Crime levels are low in Japan and murder is uncommon, however, occasional killings tend to make headlines because of their lurid nature.
In August a 16-year-old schoolgirl confessed to decapitating her classmate because she "wanted to dissect someone".