The Prime Minister said the UK would not wait until the end of any implementation period to take back full control over areas like diplomacy, peacekeeping, defence and aid.
Common policy on foreign and security areas grew out of the Maastricht Treaty so the move is likely to please Brexiteers.
But Mrs May stressed that Britain will continue to work closely with the EU on security and said the UK’s commitment to protecting Europe from threats is “unconditional”.
Mrs May said: “There is no reason why we should not agree distinct arrangements for our foreign and defence policy co-operation in the time-limited implementation period as the Commission has proposed.”
She added: “We shouldn’t wait where we don’t need to.”
The system meant that Britain was forced to take part in a summit in 2003 in Lisbon despite protesting over the attendance of Zimbabwean dictator Robert Mugagbe. Gordon Brown boycotted the event but the government was obliged to send a representative.
But in practice the UK is still expected to maintain very close cooperation.
No 10 sources insisted the move was about regaining sovereignty.
Mrs May said: “In particular, we will want to continue to work closely together on sanctions. We will look to carry over all EU sanctions at the time of our departure.
“Second, it is clearly in our shared interests to be able to continue to co-ordinate and deliver operationally on the ground.
“Of course, we will continue to work with and alongside each other. But where we can both be most effective - by the UK deploying its significant capabilities and resources with and indeed through EU mechanisms - we should both be open to that.
“On defence, if the UK and EU’s interests can best be furthered by the UK continuing to contribute to an EU operation or mission as we do now, then we should both be open to that.
“And similarly, while the UK will decide how we spend the entirety of our foreign aid in the future, if a UK contribution to EU development programmes and instruments can best deliver our mutual interests, we should both be open to that.
“But if we are to choose to work together in these ways, the UK must be able to play an appropriate role in shaping our collective actions in these areas.”
Mrs May also called for an “open and inclusive approach” on defence capability projects.
During a question and answer session German diplomat Wolfgang Ischinger sparked a round of applause from the audience of diplomats and security experts when he said it would be easier if Britain remained in the EU.
Mrs May then faced a second questioner suggesting Brexit should be ditched.
But the PM insisted Britain is leaving, adding there will be “no second referendum”.
Mrs May set out proposals for a new treaty between the UK and the EU to enshrine security cooperation and warned a reluctance to agree a new type of partnership would have “damaging” consequences.
The PM also urged Brussels to ignore the rule book and do whatever it takes to ensure the security of Europe is protected after Brexit.
Mrs May warned that “rigid institutional restrictions” and “deep-seated ideology” must not be allowed to jeopardise the safety of citizens, saying: “Those who threaten our security would like nothing more than to see us fractured.
“They would like nothing more than to see us put debates about mechanisms and means ahead of doing what is most practical and effective in keeping our people safe.
“So let the message ring out loud and clear today: we will not let that happen.”