Each podcast lasts between 25 and 30 minutes and is free to download. Users can listen to the download on their computer or transfer the file to an iPod or MP3 player.
News is read by Telegraph journalists and actors and includes Roy Greenslade's media column, sports commentary by Derek Pringle and Bill Johnson and the Ask Hilary fashion advice column.
"We are delighted that on Monday we entered the UK top 100 chart of most popular podcasts at number 21," said Annelies van den Belt, new media director at the Telegraph.
"We expect many more subscribers to sign up to the service - we've had a great response."
Newspapers have been hesistant to introduce podcasts, she said, because it's en entirely new platform.
"They have no knowledge of the production process and different skillsets are required. But we are training all journalists whose content is being used in the podcast, to enable them to 'self record'."
Introducing the new service on its website, the Telegraph cites the success of BBC Radio 4's Today podcast.
The Today podcast was launched in May 2005 as part of a wider BBC podcast trial which was averaging 100,000 weekly downloads for 20 different programmes by July.
• Blackberry users can now sign up for a free headline service from the Telegraph that delivers three updates each day. Registration is at onthego.telegraph.co.uk.
More news from journalism.co.uk:
WSJ launches Blackberry edition
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