The offer, according to the Telegraph, ranks as the biggest for a foreign takeover of a British technology firm and the largest ever Asian investment in the UK. The premium is 43% on ARM's share price on Friday.
ARM designs the microchips that power every smartphone and tablet on earth, including Apple's iPhone, and is at the forefront of developing low-power chips for the "internet of things" - connected everyday household products.
SoftBank promised to double jobs in the UK over the next five years, that ARM's headquarters would remain in Cambridge, and that its management team would stay on.
Philip Hammond, the Chancellor, said:
"Just three weeks after the referendum decision, it shows that Britain has lost none of its allure to international investors. Britain is open for business - and open to foreign investment."The sale requires 75% approval of ARM's shareholders.