The launch is expected to put in a dent in the iPhone's previously exclusive Twitter app, Tweetie, which comes with a $2.99 price tag.
TweetDeck's new desktop client will also take on Seesmic and Tweetie's recently released desktop client in the PC and Mac front.
According to TwitStat, TweetDeck is the second most popular Twitter client, used by 14% of users, behind the actual Twitter website at 26%.
Tweetie is a distant third, used by 7%, with Seesmic in eighth on 2%.
In May, Twitter had nearly 12m registered users, meaning that TweetDeck downloads could conceivably be in the 1.5m range.
The TweetDeck iPhone app is a spitting image of TweetDeck's desktop client, which features organised columns of followers, direct messages, search and @replies, that can be scanned with the swipe of a finger using the iPhone's touchscreen.
Users can now incorporate as many columns as they wish, no longer held back by a 10-column limit.
The app also allows automatic synchronisation between the iPhone and desktop clients, so that any changes made on the iPhone will be reflected on the desktop and vice versa.
Other features include multiple account support, localised Twitter trends, video playback, follower recommendations and a spam blocker.
TweetDeck, a London-based start-up, said its free-to-download iPhone app was a step closer towards its ultimate goal of filtering real-time content on the web.
Iain Dodsworth, TweetDeck founder, said: "More and more, sites are serving consumers streams of information rather than static web pages. And today's browsers aren't set up to help us filter and digest this new format. So I started TweetDeck with a focus on Twitter but a bigger vision, to become a new browser for the real-time Web. Today, we're taking a step closer to that goal."
To mark the launch, Canadian tech firm TinyMassive launched a Twitter app that helps shoppers find the lowest priced goods on the web - an online first, said the company.
By following @TinyMassive and tweeting any product search, shoppers receive a reply tweet within 30 seconds identifying the lowest price available for the product and the link to purchase.
Twitter had more than 32m unique visits in April, according to comScore, without factoring in figures from third-party clients, such as mobile phones or desktop apps.