The couple have spent their Hawaiian vacation discussing their future and are now ready to make a life-long commitment, a source told Us Weekly.
The insider added: "They have talked at length about getting married and starting a family. [Aniston] is anxious for the next phase of her life and feels like this is the time."
A friend of Aniston insisted that she has not "felt this way about anyone since Brad [Pitt]", while another of the actress's companions said: "They are moving quickly, but they know the feelings they have about [each other] are different from past romances."
Reps for Aniston and Theroux have not commented on claims that they plan to wed.
Tropic Thunder screenwriter Justin apparently introduced Aniston to his cousin Louis Theroux during a trip to London in July.
Aniston and Justin star in director David Wain's upcoming film Wanderlust, which is released on October 7 in the US and on November 25 in the UK.
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Watch Jennifer Aniston in the Horrible Bosses trailer below: