The epic adaptation of JRR Tolkien's fantasy beat the previous record-holder, Harry Potter and The Philosopher's Stone, which sold 1.25 million copies on its first day in the shops in May.
It went on to reach almost 1.6 million copies in a week, and was credited with increasing sales of players by 280% in the week of its release.
Now The Lord of the Rings' distributor is expecting bumper sales to continue after Tuesday's first day.
A spokesperson for distributor Entertainment In Video said: "This is a particularly remarkable achievement in view of the Tuesday release date for video and DVD titles.
"All major store groups have reported unprecedented demand for the title."
Extras included on the DVD include behind-the-scenes footage and a sneak preview of the second film, The Two Towers, which is due out at the end of the year.
The film follows the struggle of hobbit Frodo, played by Elijah Wood, to destroy a ring that makes its users invisible and has other dark powers.
Awards
Shot in New Zealand, it sees a series of stunning special effects-laden set pieces as the party of hobbits, humans, elves and dwarves cross Tolkien's fantasy land of Middle Earth.
Sean Bean, Orlando Bloom, Sir Ian McKellen and Sir Ian Holm were among the stars employed by director Peter Jackson.
The epic fantasy film swept this year's Baftas and MTV movie awards, although it was overshadowed by A Beautiful Mind at the Oscars.
It is the first in a trilogy based on Tolkien's much-loved books, with a total budget of £190m.
The third film, Return of the King, is due for release in 2003.