The long-running drama series will be joining the streaming service as part of Star, a new channel launching within Disney+.
All six seasons of Lost and nine seasons of 24 will be available to watch.
Star, which launches in the UK on 23 February, will broadcast content from the likes of Disney Television Studios, FX, 20th Century Studios and 20th Television.
Other new TV series additions include The X-Files, Prison Break, Desperate Housewives, How I Met Your Mother, Black-ish, Atlanta, Big Sky and Love Victor.
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A selection of titles from the Die Hard franchise will also be available to stream.
Star will be the international home of the Kardashian family’s new TV show, which was announced by Kris Jenner in December.
Following the forthcoming final season of Keeping Up With The Kardashians on E!, the family signed a new multi-year content deal with Hulu in the US, with episodes airing on Disney’s Star service in the UK later in 2021.
Disney has also announced that the price of UK subscriptions will increase to £7.99 per month or £79.90 per year from 23 February.
Existing subscribers will, however, continue to pay £5.99 per month or £59.99 per year until 23 August.
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