Warren East, 51, is to step down on 1 July and will be replaced by Simon Segars, the current group president at the Cambridge-based company.
Mr East joined Arm in 1994 to establish its consulting business and became chief executive in 2001.
He said that now was the time for a change at the top.
"Arm is a great company with a strong market position and a unique culture," he said.
"We take a very long-term view about our business, and we believe that now is the right time to bring in new leadership, to execute on the next phase of growth and to plan even further into the future."
Under Mr East's tenure Arm has become the provider of processor technology for nearly all mobile phones and many other consumer and industrial electronic devices in use today.
The company develops designs that are licensed to customers and receives royalty payments every time devices with its chips are made by its clients.
In the last 12 years it has received royalties for over 40 billion Arm chips and the company's share price has risen threefold.
Arm chairman John Buchanan said: "Warren has transformed Arm during his time as chief executive."
At the news of Mr East's departure shares in the FTSE 100 Index company fell by 3% to just under 900p.
The chief executive of Arm Holdings, whose computer chip technology powers Apple and Samsung smartphones, is retiring after 12 years in the role.