The Russian vodka brand, which was previously handled by Publicis, aims to build on its heritage and expand its target audience to include "adult trendsetters".
Ogilvy will create a new positioning, brand architecture and creative campaign for global distribution.
The appointment coincides with SPI Group's five-year plan to boost its sales internationally and particularly in the US.
SPI selected Ogilvy because of the range of ideas it presented across multiple media platforms.
Andrey Skurikhin, a co-owner of SPI Group, said: "During the pitch, Ogilvy delivered everything that Stoli needs today -- creativity, speed, flexibility, competitiveness and devotion.
"I am sure that Ogilvy's approach will be the right one to support our plans."
Carla Hendry, co-CEO of Ogilvy North America and chairman of Ogilvy New York, said: "The chance to transform the Stolichnaya brand is irresistible. Ogilvy's creativity and deep consumer insights were what led to a creative idea that we believe will allow Stoli to reach new heights as the vodka market continues to expand."
Ogilvy's first work for Stoli is expected before the end of this year.