Sources said that the presence of Sceptre around the Falklands is hoped to be enough to dampen the ambitions of Argentina - which still lays claim to the British islands.
Details of the submarine's deployment came as speculation soared that British firm Desire Petroleum has struck oil, sending its share price sky-high.
Desire - the first company to explore there - is expected to announce next week whether it has had success.
The company is the first of seven British-backed firms hoping to drill there in the coming months. Experts claim there could be as much as 60 billion barrels of crude under the Falklands' coastal waters.
But any discovery will dramatically increase the tension between the UK and Argentina.
Argentina's President Cristina Kirchner insists that the Falklands are occupied by Britain illegally and she has tightened shipping regulations.
Last Wednesday a mob of 100 protesters armed with petrol bombs were stopped by cops as they tried to storm the British Embassy in Buenos Aires.
It is understood that HMS Sceptre - which is equipped with Spearfish anti-ship torpedoes - sailed south from the coast of southern Africa last month.
Its mission in the South Atlantic is to monitor the disputed so-called "Conservation Zone" waters surrounding the islands - where drilling is currently under way.
The Ministry of Defence refused to discuss Sceptre's deployment.
A spokesman insisted "We do not comment on submarine operations."
But a source told The Sun "HMS Sceptre is a fully-equipped, nuclear-powered submarine.
"It has state-of-the-art listening sensors and will be monitoring all ship movements in the area. The decision to send HMS Sceptre was made last month and it has taken more than three weeks to reach the area.
"The mere fact she is lurking somewhere in the waters around the islands will strike fear into the hearts of any possible enemy."
Naval expert Steve Bush, editor of Warship World, described the benefits of having a submarine in the area.
He said "A nuclear-powered submarine has been dispatched.
"They are vessels capable of reconnoissance, monitoring and anti-strike shipping missions if required.
"While there it will remain underwater, totally stealthy. They will remain invisible.
"They will not know where it is, and that is the threat."
Last month we told how Type 42 destroyer HMS York was patrolling off the islands' capital Port Stanley.
It has been joined by the survey vessel HMS Scott.
The fleet also has air support from a squadron of RAF Typhoon fighter jets based on the islands.