The car was bought by Rick Champagne, a logistics company owner from Phoenix, Arizona.
The 56-year-old, who was just 10 when the high-camp TV series began in 1966, said it "was a dream come true".
The Batmobile design was based on a 1955 Lincoln Futura, a concept car built in Italy by the Ford Motor Company.
It was the first time that car had come up for public sale since it was bought in 1965 by car-customiser George Barris for a nominal fee of $1.
Barris then spent $15,000 (roughly £5,370 at the time) to transform it into the famous superhero vehicle, over a period of 15 days.
It had a V-8 engine,  arguably one of the first in-car phones, and parachutes, which were deployed to help Batman turn sharp corners.
Mr Barris told reporters at the auction: "The car had to be a star on its own. And it became one."
Since the show was cancelled in 1968, he  has toured the Batmobile and was eventually housed in a private showroom in California.
Adam West,  now 84, played the caped crusader in 120 episodes in four years of programming, with Burt Ward starring as the "boy wonder" Robin and comedian and actor Cesar Romero as Batman's arch nemesis, The Joker.
The 60s show was camp in its portrayal of Batman. More recent incarnations of billionaire Bruce Wayne and his alter-ego - such as British director Christopher Nolan's Dark Knight trilogy  - have had a much darker tone.
The newer Batmobiles have reflected the more brutal portrayal of Gotham City's saviour, such as the "Tumbler" of 2005's Batman Begins, starring Christian Bale.
The Batmobile used by actor Adam West in the original TV series of Batman has sold for $4.2m (£2.6m) at a US auction.