The BBC's Spain correspondent Flora Botsford says that the departure of the Tireless will be a relief to the Spanish Government, which has been left in an awkward position since its arrival in Gibraltar.
The presence of the HMS Tireless in Gibraltar caused outrage among environmentalists and strained relations between Spain and the UK.
The submarine left the harbour on Monday morning accompanied by Royal Navy patrol vessels and protesters who had gathered for its send off.
The British military has not said where the Tireless is heading now, but it is believed to be destined for a port in the UK.
Protests
The submarine was brought in for repairs after a crack was found in a cooling pipe near its nuclear reactor, sparking fears that it could leak and contaminate the environment.
The BBC's Spain correspondent Flora Botsford says that the departure of the Tireless will be a relief to the Spanish Government, which has been left in an awkward position since its arrival in Gibraltar.
While Prime Minister Jose Maria Aznar tried to listen to people's concerns about the vessel, he was keen to maintain his special relationship with the British leader Tony Blair.
Although the UK insisted that the submarine posed no risk to the local population or environment, it removed 12 similar submarines from service to check if the crack had been caused by a design fault.
People in Gibraltar and in southern Spain staged regular protests against the Tireless and it has been the subject of a high-profile direct action campaign by the environmental organisation Greenpeace.