The format launched in the UK in December last year and features topics that people are Tweeting about.
The stories, collated by the social network’s editorial team, can be accessed by clicking the lightening bolt symbol on the Twitter app.
Users can read more on a topic by swiping left and will see new Promoted Moments in their feed.
Tesco is the first UK brand to launch a campaign on Promoted Moments today.
The activity, called "#FeelGoodCookbook", was created by Bartle Bogle Hegarty. It features videos and images with recipe ideas that users can flick through like an e-book. Tesco will also pin the cookbook to the top of its Twitter profile. Media planning and buying was handled by MediaCom.
Xbox’s campaign will be about Quantum Break, a new game. Sky has yet to announce the focus of its activity.
This month, Twitter launched Conversational Ads, which allow brands to create ads that can be personalised by users.
Twitter’s UK pre-tax profits almost doubled to £3.3 million in 2014, with its UK ad business growing almost twofold during that period.
The company began testing Promoted Moments in the US in October last year.