Motorola has so far purchased 10 per cent of the company's shares, with the rest due to be tendered before the end of the year.
"The offer by Motorola Solutions provides Psion's shareholders with certainty in an environment where certainty is in short supply," said Psion chairman John Hawkins in a statement.
Psion made the world's first personal digital assistant in 1984. The device, called the Psion Organiser, was released the same year as Apple's first Macintosh computer and could handle such functions as storing contacts, managing a digital diary and doing calculations.
In 1998, a partnership between Motorola, Nokia and Ericsson to develop a smartphone platform led the Psion operating system to be renamed Symbian. Nokia bought out Symbian in 2004, but switched to Windows Phone in 2011 amidst lagging smartphone sales.
"Psion is a compelling opportunity to strengthen our industry-leading, mobile-computing portfolio with ruggedised handheld products and vehicle-mount terminals," said Motorola CEO Greg Brown.
Motorola recently sold its Mobility arm to Google in a $12.5 billion (£8 billion) deal.