Tweets can already be published elsewhere on the web using aggregation tools like Storify, or publishing tools like Fabric or Twitter for Websites. However, the difference is that paid-for Tweets can now be embedded into partner sites alongside regular Tweets.
The service offers an additional revenue source for media owners and, according to Twitter's blog, "provides great content and monetisation opportunities for our syndication partners".
Twitter gave the example of a Nissan campaign replicating the creative and targeting in its Twitter activity in other environments that feature organic Tweets, such as in the Flipboard app.
As more partners join the trial, promoted Tweets could be expanded to any kind of digital publisher or device, from TVs to websites to mobile apps.
In its blog about the launch, Twitter said: "For the thousands of brands already advertising on Twitter, these new partnerships open a significant opportunity to extend the reach of their message to a larger audience."
Twitter's move gives the company opportunities that have some parallels to Facebook's Atlas ad product, which allows advertisers to use Facebook's data to target consumers outside the platform.
The launch comes ahead of the company's earnings call on Thursday 5 February.