Tweet this: Twitter has acquired TweetDeck, the company behind an app and desktop client that imposes order on the chaos of tweets, for $40 million, CNNMoney is reporting, though there are doubters in the face of previous false alarms.

Rumors have been swirling for months about a potential purchase of TweetDeck, which helps users view and manage those 140-character tweets, by Twitter though for a much higher price: $50 million.

CNNMoney said: “The deal has yet to be announced, but papers finalizing the deal were signed Monday.”

Mashable was skeptical because there have been a string of such rumors that have failed to materialize. “(Given) the history of the Twitter/TweetDeck acquisition story, we’d be hard pressed to say, ourselves, if the deal has actually been signed and sealed,” Mashable said. “Last time this rumor came up, TechCrunch was reporting the deal would be announced within the week. That was about three weeks ago.”

San Francisco-based Twitter tweeted: “For all those who might be curious, we continue to not comment on rumors.”

Meanwhile, under the headline, “Deal Done,” TheNextWeb.Com said: “This purchase fuels speculation that Twitter is looking to improve its offerings for power users.”

TweetDeck was founded in London with about $4 million in funding from The Accelerator Group and Betaworks.

Twitter in the past has purchased about a half dozen third-party apps, including iPhone app Tweetie, and partnered with photo app TwitPic.

TheNextWeb said: “Since Ev Williams left Twitter and Jack Dorsey took over as the company’s CEO — both of them co-founders — the company has focused on building the feature set that the majority of users have found lacking in the company’s own web client, which lead to the mass adoption of a range of third-party clients. TweetDeck was the most popular of them all.”

Mashable said: “The relationship between TweetDeck and Twitter has been tense of late. Around 40 percent of tweets come from third-party apps, and TweetDeck is a leader in the third-party category. And Twitter itself has been giving devs none-too-subtle hints that it doesn’t want its API being used for pure-play Twitter clients anymore.”

The Wall Street Journal reported that Twitter, with more than 200 million registered accounts, has been aiming to broaden its appeal by making it easier for new users to navigate messaging service easier and helping longtime users find useful content.