Mr de Geer said: "Combining our assets and expertise with a global industry leader like PayPal allows us to deliver even more value to small businesses to help them succeed in a world of giants."
PayPal boss Dan Schulman called the purchase a "strategic fit, with a shared mission, values and culture – and complementary product offerings and geographies".
"In today's digital world, consumers want to be able to buy when, where and how they want," he said late on Thursday.
iZettle provides credit card readers to many small businesses across South America and Europe, but has also been expanding into software and financing services, while PayPal has been looking to widen its presence in the point-of-sales payments market.
Although iZettle is still posting losses – in the first quarter of 2018, it reported negative earnings before tax, depreciation and amortization of SEK73 million ($12.1m) – it has been moving closer to profit, and iZettle and PayPal said financial benefits would feed through from the deal later this year.
In a joint statement, the pair said iZettle was expected to generate revenue of US$165 million this year, compared to US$89 million last year.