In addition, listeners will be able to read every castaway's choice of music, books and luxury items on the site.
Presenter Kirsty Young will also curate a series of 'classic editions' of the long-running radio show on the broadcaster's rebranded station BBC Radio 4 Extra.
She said: "Desert Island Discs occupies a special place in many listeners' hearts - its enduring popularity throughout the decades testifies to that.
"I'm really delighted that BBC Radio 4 Extra will give people the chance to hear even more of the show and the launch of the new website means everyone has the chance get their hands on the Desert Island Discs archive and hear the music, book, luxury and lives of hundreds of castaways from programmes gone by. A real treat."
Extended repeats of shows from the past year will also be broadcast on BBC Radio 4 Extra when it launches in April.
Tim Davie, the BBC's director of audio and music, said: "I'm delighted to announce the launch of BBC Radio 4 Extra and hope that fans of Desert Island Discs will indulge themselves in the previously-buried treasures of vintage episodes."
The online archive will also launch in April.