Flights will run twice a week from November 2 with one-way fares starting at £24.99.
The service will operate on Wednesdays and Sundays.
Wizz Air UK managing director Marion Geoffroy said: “We are pleased to announce the addition of another exciting route from our base at London Luton Airport, as we offer our customers even more choice for their holidays.
“Podgorica serves as the perfect destination for customers looking to discover a new city that is not only filled with fantastic museums but is surrounded by picturesque national parks”, local media reports.