The station now holds records for the longest broadcast of a single piece of music and the longest live broadcast of a single piece of music.
Richter and an ensemble of six musicians played non-stop throughout Saturday night and were broadcast live from London's Wellcome Institute.
A live audience slept in camp beds.
Listeners at home were also encouraged to sleep through the broadcast.
BBC reporter Emma Jane Kirby, who was there, said: "Like a lullaby on a loop, the musical themes were insistent and persistent - and I found myself drifting out of consciousness."
The new records were certified by Guinness World Records.
Described as a "lullaby for a frenetic world", Sleep was composed in consultation with neuroscientist David Eagleman.
Richter told BBC Breakfast: "I, personally, am very lucky that I sleep well but I know I'm quite unusual.
"We're kind of a sleep-deprived culture now, our world is very busy, we live in a data blizzard and we're on 24/7 and people sometimes find it difficult to find a space to rest and that's what this is."
The broadcast formed part of Radio 3 and Wellcome Collection's Why Music? weekend, a series of programmes linking musicians with leading scientists investigating music's role in life.
Radio 3 controller Alan Davey said: "To establish two new world records with one broadcast overnight is a shining example of what makes us so unique.
"It's rare a controller wills his audience to sleep, but I hope Radio 3 listeners enjoyed slowing down to Max Richter's Sleep.  I'm grateful to Max Richter for working with us on this great project."
The broadcast will be available to listeners on BBC iPlayer for 30 days.
BBC Radio 3 has set two world records after broadcasting a live performance of composer Max Richter's eight-hour composition, Sleep.