Mr Winstanley said that buying Sansa Security, which calls itself "the only comprehensive IoT security platform", was a "key strategic acquisition".
He also praised Israel for its "fantastic expertise" in technology, and said that the move to open what Arm has termed "a global design centre" in the country would be mutually beneficial.
"This is our first engineering presence in the country. It's positive and hopefully positive for Israel as well. We intend to grow the number of people we have there, as we see it as an exciting location where we can maintain our commercial presence and build a new engineering capability."
Coby Sella, chief executive of Sansa Security, said in a statement: "Joining Arm will enable us to scale the business by helping Arm's global technology partners to address their most pressing security needs."
Mr Sella pledged that the deal would allow his company "to develop our products and capability to new levels".
The sale is just one example of Israel's successful cyber-security sector, which for the first time has reported sales that exceed the country's exports of military weapons. The £3.8 billion figure represents a tenth of global cyber-security sales.
