The two shows, which are among Channel 4's biggest ratings successes, will be made available at a cost of 99p for unlimited viewings during a 24-hour period through the channel's website .
The deal also involves NTL/Telewest, which has secured the rights for the two dramas to be shown in high definition format.
The move falls short of a full video-on-demand service, which has been put on hold due to negotiations about non-linear rights with independent producers group Pact.
A spokeswoman for Pact confirmed that the negotiations were still ongoing and if a deal was not reached by the end of May, media regulator Ofcom will intervene and impose its own decision. This will affect a raft of other hit shows including Endemol's 'Big Brother', which begins its annual run this summer.
Andy Duncan, Channel 4 chief executive, said: "By partnering exclusively on the video-on-demand rights to two of the biggest shows on TV, we will work together to reach and grow on-demand audiences.
"The deal reinforces Channel 4's plans to make content available anytime, anywhere, and is a fantastic way of demonstrating our ambitions in this area."
Rod Henwood, Channel 4's new-business director, added: "This is a significant step in Channel 4's plans to launch a video-on-demand service across multiple platforms later this year. Partnering with Disney on these two stand-out shows illustrates the critical strategic importance of video on demand to Channel 4."
'Lost' series one will be available from this week, with episodes from series two, which starts on Channel Four on May 2, available 14 days after their first UK broadcast.
To promote the service, Channel 4 is offering viewers the first two episodes free of charge.
On-demand episodes of 'Desperate Housewives' series two will be available from May 4, with series one available a month later.
If you have an opinion on this or any other issue raised on Brand Republic, join the debate in the .