The countries covered by this move include Australia, New Zealand, Japan, Bangladesh, the Sultanate of Brunei, Cambodia, India, Indonesia, South Korea, Laos, Malaysia, Nepal, Pakistan, the Philippines, Singapore, Sri Lanka, Thailand, and Vietnam.
The firm undertook what it calls a Global Transparency Initiative in 2018 to prove its bona fides after the damaging American propaganda campaign, which led to it losing all its business with the US public sector.
A new centre for data storage has been opened in New Brunswick, Canada, to add to existing centres in Sao Paulo and Kuala Lumpur, where partners are given the chance to examine the source code of its products.
Allegations were regularly made that it had been serving as a conduit for Russian intelligence services and the accusations gathered momentum as Moscow was claimed to have interfered in the 2016 US presidential election, a charge that was proven to be false after a two-year investigation by former FBI director Robert Mueller.
Kaspersky's initial timetable was to complete the move of operations from Australia, North America, Europe, Singapore, Japan and South Korea to a data centre in Zurich by the end of 2019. That appears to have been delayed by about a year.
The American allegations led to the Netherlands announcing a similar ban, while the UK's National Cyber Security Centre also advised agencies and organisations against using the company's software.
In a statement issued on Wednesday, Kaspersky said: "The customer threat-related data shared by ANZ customers and partners are now processed in two data centres in Zurich, including detected suspicious or previously unknown malicious files that the company’s products send to the Kaspersky Security Network for automated malware analysis."
Kaspersky chief executive Eugene Kaspersky said in a statement: “Since we announced our Global Transparency Initiative with a number of bold steps, including data-processing and storage relocation, Kaspersky has not only reconfirmed its commitment to being a trusted partner, but anticipated expectations from the market and regulators.
"In the three years since the announcement we have seen the major transformation of approaches and regulations in data security. We see that investment in trust and transparency is gradually becoming an industry standard, and I am proud of our company for being among the transparency pioneers and trailblazers.”
Kaspersky ANZ general manager Margrith Appleby added: “For 23 years, Kaspersky has remained at the forefront of developing cyber-security technologies and with this announcement we continue to build trust and transparency with our customers and partners.”
The company also pointed to its other projects, including improvements to its cyber capacity building program announced in May, adding that the product scope for its Bug Bounty Program had been extended to include Kaspersky VPN Secure Connection.
"Researchers can now submit vulnerability reports relating to Kaspersky VPN Secure Connection, including third-party software modules that are a part of the VPN solution. Overall, since March 2018, within the Bug Bounty Program, 76 bugs have been resolved, and 37 reports rewarded with total bounties equating to US$57,750 (A$79,063)," the company said.