The Ugly Betty star will play Roxie Hart in the musical, beginning on November 7, according to Entertainment Weekly.
Previous stars to have appeared in the London edition include Denise Van Outen, Michelle Williams and Jennifer Ellison.
Once Ferrera completes her run in London, she will then make her Broadway debut in a revival of Beth Henley's 1984 play The Miss Firecracker Contest.
The play revolves around a Mississippi woman who enters a beauty pageant. She will begin rehearsals in March, with a premiere scheduled for the spring.
The actress will appear in ensemble indie comedy It's a Disaster alongside Rachel Boston and Todd Berger next year.