The pair were found inside Devonport Naval Base, Plymouth, at about 1130GMT on Friday.
A Ministry of Defence spokeswoman said Petter Joelson from Sweden and Elisa Silvennoinen from Finland had been remanded in custody to appear before Plymouth magistrates on Monday.
They were arrested at 9 Dock, where the Trident submarine HMS Vanguard is currently undergoing a re-fit.
In a statement anti-nuclear campaigners alleged the couple had got onto the submarine and rung its bell.
A perimeter fence and a fire alarm were reported to have suffered minor damage during the break-in.
The campaign group Trident Ploughshares is currently holding a four-day "peace camp" in Plymouth.
A statement released by the group on Saturday said its activists had entered the naval base, showing MoD security to be "woefully inadequate."
A Royal Navy spokeswoman said the pair had been found on the submarine.
'Lax security'
The Ministry of Defence Police, Devonport Management Ltd (DML), which runs the dockyard, and the civil police are investigating the incident.
In a statement the MoD said wider safety issues were not compromised by the incident.
Ian Martin, South West spokesman for CND, said: "I convey my congratulations to this latest Trident Ploughshares initiative which exposes the absurdity of Trident. It should be scrapped, not re-fitted."
HMS Vanguard, which arrived at Devonport in February this year, is one of seven nuclear-powered submarines based there.