A jury at Snaresbrook Crown Court, in east London, took less than 30 minutes to find the 22-year-old club promoter not guilty of two counts of raping the woman at his home on 4 September last year.
The allegations were "scurrilous and completely groundless", Mr Tweed said as he left court. His friend Anthony Davis, 26, a property developer, was also cleared of one count of raping the girl, who was 19 at the time of the incident.
Mr Tweed issued a statement through his solicitor, Philip Smith, which read: "I'm relieved that the jury have taken a matter of minutes to see through these scurrilous and completely groundless allegations.
"I now want to put the last eight months behind me."
There were roars of delight from a packed public gallery as the verdicts of not guilty were returned.
The jury heard the young woman, now a 20-year-old student from Hertfordshire, went with friends to Mr Tweed's house in Brandesbury Square, Repton Park, Woodford Green, east London, after a night out at the Embassy Club in Mayfair.
Mr Tweed and Mr Davis, of Stradbroke Drive, Chigwell, Essex, both denied rape.