The board of ARM is expected to recommend shareholders accept the offer - which is around a 43% premium on its closing market value of 16.8bn pound on Friday.
The Cambridge-based firm designs microchips used in most smartphones, including Apple’s and Samsung’s.
ARM, which was founded in 1990, employs more than 3,000 people.
Shares in the UK technology firm surged by 45% at the open of the London Stock Exchange to 1,742.85p per share, adding 7.56bn pound to ARM’s market value.
Japanese entrepreneur
ARM said it would keep its headquarters in Cambridge and that it would at least double the number of its staff over the next five years.
Softbank is one of the world’s biggest technology companies and is run by its founder, Japanese entrepreneur Masayoshi Son.
It has previously acquired Vodafone’s Japanese operations and the US telecoms company Sprint. The $20bn deal was the biggest foreign acquisition by a Japanese firm at the time.
The new deal will be funded by Softbank’s own cash reserves and a long term loan from Japan’s Mizuho Bank.
’Sad day’
Softbank intends to preserve the UK tech firm’s organisation, including its existing senior management structure and partnership-based business model, ARM said.
Masayoshi Son, chairman and chief executive of Softbank, said: "This is one of the most important acquisitions we have ever made, and I expect ARM to be a key pillar of SoftBank’s growth strategy going forward.
However, the co-founder of ARM Hermann Hauser said: "This is a sad day for me and a sad day for technology in Britain."
"ARM is the last British [technology] company that has a global reach," he said.
"It gave Britain real strength. It was a British company that determined the next generation microprocessor architecture."
’Attractive destination’
Prime Minister Theresa May said the deal between Softbank and ARM Holdings showed the UK economy could be successful after the country voted to leave the European Union.
A spokeswoman for the prime minister said Mrs May believed the deal was in the country’s national interest - a gauge that she will use to assess any future foreign takeovers.
"This is good news for British workers, it’s good news for the British economy, it shows that, as the prime minister has been saying, we can make a success of leaving the EU," the spokeswoman added.
Dan Ridsdale, analyst at Edison Investment Research, said "An increase in inbound merger and acquisition activity was one of the obvious consequences of Brexit and weakened sterling, but few expected it to manifest itself so quickly or at so large a scale."
Former Business Secretary Vince Cable told the BBC there was usually very little the government could do to prevent takeovers.
"We don’t have a system of defence against takeovers if they prove to be unsatisfactory," he said.
Mr Cable added the government had few legal powers to stop takeovers unless it could be demonstrated there was a national security issue.