The Oscar-winning star will run the new company and make a "significant" time commitment for the job - but will not give up making movies.
"
I really don't want to spend my life doing a movie, movie, and then a play here and there - this gives me a purpose
"
Kevin Spacey
He was revealed as the company's director by the theatre's chairman, Sir Elton John, on Wednesday, and will be a vital figure in raising money to keep the troubled 185-year-old theatre open.
The announcement came before a fund-raising gala concert in which stars including Sting, Elvis Costello and Sinead O'Connor performed Sir Elton's songs.
Spacey said the theatre was his "primary allegiance" but that he would not abandon the United States.
He would appear on stage at least twice and direct plays, he said.
"I do not underestimate the level of commitment this project is going to require of me," he said.
"It is something that I feel deeply about, have put over two years of thought towards and frankly is something I am utterly overjoyed at having reached a decision upon."
Spacey, who has won Oscars for The Usual Suspects and American Beauty, fell in love with the Old Vic after being taken there during a childhood holiday.
He appeared on the Old Vic stage in 1998, and has been heavily involved in fund-raising and running the theatre since becoming a trustee that year.
The actor was said to have flown to London regularly to attend board meetings, and has invested more than £100,000 of his own money into the venue.
"
He's so passionate and I believe in it so much - that's why I joined as
chairman
"
Sir Elton John on Kevin Spacey
The Southwark-based Old Vic is one of London's oldest theatres, having opened in 1818.
It has played host to performances from Sir Laurence Olivier, Sir John Gielgud, Sir Alec Guinness, Vivien Leigh, Peter O'Toole and Dame Judi Dench.
The 1,000-seat theatre was saved from property developers by impresario Sally Greene in 1998 but still needs millions of pounds to ensure its survival.
As well as having financial difficulties, it has also struggled with a leaking roof, mould and cracks in the walls.
Sir Elton and Spacey were joined by trustees Lord Attenborough and director Stephen Daldry at Wednesday's press conference.
"
I feel strongly that no matter what events we have, as long as there are people who have a story to tell and there are people who will listen, theatre will be alive and well
"
Kevin Spacey
Sir Elton said: "Kevin's talent is exceptional, but what has truly inspired me is his passion for, and commitment to, this theatre.
"I know that under his leadership a permanent company at the theatre will bring a totally new dynamic so that the Old Vic remains one of the most important theatres in the world."
Also present was former ITV director of programmes David Liddiment, who will be producer of the new company.
Wednesday's concert was expected to raise more than £700,000, with the audience paying up to £1,000 each for tickets.