The Japan international spent the last campaign with the German side and helped them win the second division.
That led to Stuttgart gaining promotion to the Bundesliga and now the 22-year-old will join them for the challenge next season.
Asano joined Arsenal from Sanfrecce Hiroshima last summer, but was sent to Germany on loan after failing to gain a work permit.
The forward bagged four goals for Stuttgart over the course of last season.