Budimlija, who has worked at M&C Saatchi for the past nine years, will join the agency in the summer, where she will head up and build its strategy and planning departments.
Nitro has been without a head of planning since its launch in 2004.
After its acquisition of Soul last year, Kevin Brown, one of Soul's founders and its planning chief, left the merged agency. He has subsequently joined Bartle Bogle Hegarty.
While at M&C Saatchi, Budimlija worked across various accounts and led planning on Transport for London.
Bruce Crouch, the Nitro partner and joint executive creative director, said: "We felt Verra was talented and capable of building our planning department now that there is a 360-degree offering in place. We value strategy and planning very highly. We are genuinely delighted to have her on board."
Paul Shearer, Nitro's other partner and joint executive director, said: "Verra will be someone we will learn from. She is a creative planner with a mature focus and she has bags of common sense."
Nitro's clients include Coca-Cola, Nike and Drambuie. DM clients include Royal Bank of Scotland and digital clients include Sony PlayStation and Diesel.