The 90-year-old monarch formally opened the London hub alongside her husband Prince Philip, 95, and a host of government ministers including finance minister Philip Hammond.
"The cyberattacks we are seeing are increasing in their frequency, their severity, and their sophistication," Hammond said at the official opening.
"In the first three months of its existence the NCSC has already mobilised to respond to attacks on 188 occasions."
The finance minister vowed to "invest the necessary resources" and called for a "team effort" to counter the attacks against businesses and individuals.
The centre is one element of a £1.9 billion ($2.38 billion, 2.24 billion euros) government strategy unveiled in November to tackle cyber threats.
As part of its bid to tighten security, the government is opening 100 posts at the new hub to be filled by private sector employees on secondment from their permanent jobs.
The Duke of Edinburgh joked to staff that it was important "to hire more people who do not predate the internet," according to an official NCSC tweet.
Part of Britain's communications spying agency, GCHQ, the London hub is aimed at implementing preventative measures such as better securing state websites and email accounts.
At the opening, agency chief Robert Hannigan said "this morning began a new chapter in nearly 100 years of GCHQ's service to the country."
Staff are also preparing for a major "category 1" cyberattack, which is expected to happen sooner or later, CEO Ciaran Martin said in a Sunday Times interview.
The centre chief accused Moscow of targeting political institutions and parliamentary organisations in incidents "well evidenced by our international partners".
"Over the last two years there has been a step change in Russian aggression in cyberspace," he told the newspaper.
Martin's comments come after US intelligence agencies accused Moscow of interfering in the country's November elections, which prompted the outgoing administration to impose sanctions on Russian agencies.
Cyberattacks on government departments seek information on policy, including energy and diplomacy, while state-sponsored attacks on companies can be aimed at stealing intellectual property, Martin said.