SodaStream Chief Executive Daniel Birnbaum said the deal would open new markets to his company through PepsiCo's global distribution and marketing network, adding that the company would keep its operations in Israel.
Founded in the United Kingdom in 1903, SodaStream was a coveted device in British kitchens in the 1970s and 80s, allowing customers to create fizzy drinks by adding flavoured syrups to carbonated water, but it faded in popularity as soft drinks became cheaper.
Israeli-based SodaStream listed on the NASDAQ in 2010.
The deal, announced on Monday, sees PepsiCo paying $144.00 in cash for each SodaStream share, a 32% premium to the 30-day volume weighted average price.
"Daniel and his leadership team have built an extraordinary company that is offering consumers the ability to make great-tasting beverages while reducing the amount of waste generated", Nooyi said in the statement.
Ramon Laguarta, who will take over from Nooyi as PepsiCo boss later this year, said: "SodaStream is highly complementary and incremental to our business, adding to our growing water portfolio, while catalyzing our ability to offer personalized in-home beverage solutions around the world".
She said SodaStream's products, which are marketed as a healthy alternative to sugary drinks, fit in with the United States firm's goal of "making more nutritious products while limiting our environmental footprint".
"Together, we can advance our shared vision of a healthier, more-sustainable planet", she said.
In 2015, SodaStream shut down a plant in the West Bank following a boycott campaign that included targeting Hollywood actress Scarlett Johansson after she advertised its product.
The purchase, which is expected to close by January 2019, will see PepsiCo, most famous for the Pepsi soft drink, acquire a company that specializes in the production of home fizzy drink dispensers.
SodaStream is available at more than 80,000 individual retail stores across 45 countries.