Film minister Shaun Woodward said the scheme ensured that "vintage and rarely-seen films are now no longer the preserve of the arthouse cinema-goer".
"This is a fantastic resource for the public who will now, more easily, get to see films from a bygone era."
'Social record'
There are 21 downloads available in the first wave of content, with new additions to follow each month.
Rarities include South, a 1919 silent documentary about Sir Ernest Shackleton's expedition to Antarctica; Michael Powell's 1937 film The Edge of the World; and more recent works featuring Doctor Who actors David Tennant and Christopher Eccleston.
"Film and television are a social record, a historical resource [and] a chance to travel through time," said BFI director Amanda Nevill.
"We are well on the way to meeting the challenge of opening up this extraordinary resource even more."