The duo have yet to openly acknowledge their romance, but Theroux has touted Aniston as the "classiest lady" that he knows and is to believed to have recently been introduced to many of the Horrible Bosses star's close friends.
Theroux and Aniston arrived together at LA's SoHo House for a party following the MTV Movie Awards on Sunday and spent much of the night at each other's side as they chatted with fellow celebrities, a source told Us magazine.
The pair apparently shared several kisses, including a passionate embrace just before they exited the event.
A second insider described Aniston and Theroux's demeanour, remarking: "[There was] lots of sexual tension. She [has] never seemed happier."
Aniston accepted the 'Decades of Hotness' prize the previous evening at the Spike TV Guys Choice Awards gala at LA's the Sony Pictures Studios.
Horrible Bosses is released on July 8 in US cinemas and on July 22 in the UK.
Watch the Horrible Bosses trailer below: