The pair, both 24, had intended to "kill several people at Helsinki University", prosecutors said, and were found in possession of munitions, a crossbow and ingredients for the manufacture of toxic gas, as well as child pornography.
The man, who claimed the plot was a way to express his anger at having been bullied at school, was jailed for three years and one month. The woman, who gave a Nazi salute at the start of the trial, received three years. Both denied intending to kill.
According to local media, the pair were reported to police after details of their plot surfaced online.
The court heard that they intended to obtain firearms by looting an armoury and then kill up to 50 people on the university campus.
They also planned other attacks, such as taking hostages, torching buildings and releasing toxic gas in public.
In 2007, a gunman killed seven students and the headmistress of a high school north of Helsinki. The following year a gunman shot dead 10 people at a technical college in western Finland. Both committed suicide.