The individuals and all members of their households have been ordered to self-isolate after one case was detected in Essex and the other in Nottingham.
Both cases are believed to be connected and there is a link to southern Africa.
Sajid Javid told BBC News: "Today I can announce one thing that we are doing immediately is carrying out targeted testing and sequencing of positive cases in the two areas that are affected."
The Health Secretary said anyone who has travelled to Angola, Mozambique, Malawi or Zambia in the past 10 days should take PCR tests.
“We know there’s this new variant out there. We don’t know enough about it yet but from what we do know, the protections that we have - especially the vaccines - are hugely important,” he added.
We have been made aware by @UKHSA of two UK cases of the Omicron variant. The two cases are linked and there is a connection with travel to southern Africa.
These individuals are self-isolating with their households while further testing and contact tracing is underway.
— Sajid Javid (@sajidjavid) November 27, 2021
Asked if the cases could spark new Covid restrictions, Mr Javid said: “We will do whatever is necessary to protect the progress we have made as a country. We’ve come a long way since the summer and we keep all of this under review and if we need to take further action, we will.”
Prime Minister Boris Johnson is expected to set out further measures during a Downing Street press conference later on Saturday.
A spokesperson for Essex County Council said: "We can confirm that a single case involving the new Covid-19 Variant of Concern (B 1.1.529), Omicron, has been identified in Brentwood.
"This is linked to a single case from Nottingham involving international travel to South Africa.
"We are working with regional and local public health officers who are assessing the situation.
"All close contacts of these individuals will be followed up and requested to isolate and get tested.
"The individuals who have so far tested positive, as well as all members of their households, are being re-tested and have been told to self-isolate while contact tracing is under way.
"While this work takes place, it is important that everyone takes sensible precautions - get a PCR test if you have symptoms, isolate when asked, wear a face-covering in crowded and enclosed spaces, ventilate rooms, get your vaccine and boosters as soon as you can."
England’s chief medical officer Professor Chris Whitty said: “We will continue to work closely with the international community to quickly gather and analyse information on this variant to understand any possible increase in transmissibility or resistance to vaccines.”
The UK is the second European nation to have reported the presence of Omicron after Belgium said it had identified a single case on Friday.
Ministers said non-UK and Irish residents who have been in Malawi, Mozambique, Zambia and Angola in the previous 10 days will be refused entry into England from 4am on Sunday.
Those who are permitted to return will be ordered to isolate in a Government-approved facility for 10 days.
South Africa, Botswana, Eswatini, Lesotho, Namibia and Zimbabwe were added to the red list on Friday. The UK also imposed a ban on flights leaving from those nations.
"The UK Health Security Agency is carrying out targeted testing at locations where the positive cases were likely to have been infectious," the Government said.
"In response to the developing situation, the UK is taking decisive action to protect public health. Confirmed cases and contacts are being followed up and requested to isolate and get tested as necessary."
“It may also impact the effectiveness of one of our major treatments,” he told the House of Commons.
He said the variant was of “huge international concern” and it was “highly likely” it had spread to other countries.
“We are concerned that this new variant may pose substantial risk to public health. The variant has an unusual large number of mutations,” he said.