Sony is paying 1.1bn Euros (£964m) for the remaining 50% stake of Ericsson, making the mobile phone business a wholly-owned subsidiary of Sony.
As part of the deal, Sony will get five sets of patents that are essential to making Sony Ericsson phones.
The tie-up had long been expected, as Sony was keen to integrate its mobile phone division with its games console and tablet computer businesses.
"This acquisition makes sense for Sony and Ericsson, and it will make the difference for consumers, who want to connect with content wherever they are, whenever they want," says Sony's chairman Sir Howard Stringer.
Last month Sony started selling its iPad-rivalling Tablet S, launched at IFA in Berlin.