President Emmerson Mnangagwa has approved the bill after it was voted through in parliament last week. Zimbabwe currently has around 60 death row prisoners.
The last time the death penalty was carried out in the country was in 2005.
President Mnangagwa has long advocated for the abolition of the death penalty. He himself was sentenced to death for blowing up a train during the civil war in the 1960s. The sentence was later commuted to ten years' imprisonment.
Amnesty International describes the abolition of the death penalty in Zimbabwe as a "glimmer of hope". Kenya, Liberia, and Ghana have also recently taken "positive steps" towards abolishing the death penalty, according to the organization.