BBC+ is available on iOS and Android. It brings together news, iPlayer content, weather forecasts, recipes and more.
Users must have signed up for an account, which lets the BBC track their use of the software.
One expert questioned how much appetite there would be for the service.
It is the 15th app to be offered by the BBC, excluding those launched by its commercial arm BBC Worldwide.
"This follows a growing trend to have a super app which is a one-stop destination for a broad range of content and services," said Paolo Pescatore, from the CCS Insight consultancy.
"But the BBC, like others, needs to be very careful it does not overwhelm its customers with too many apps.
"Research has shown that there is growing 'app-athy' amongst consumers who can't cope with the sheer number of apps they end up with on their phones.
"The danger is that they use an app once and never return to it as it gets buried amongst other apps already installed - that is terrible for long-term consumer engagement."
The BBC recently announced one of its other apps - BBC Newsbeat - would soon close, and its youth-focused content would be rolled into the main BBC News app.
That decision was made, in part, because it had not attracted as many users as hoped.
"Audiences... are telling us that, online, BBC News is the brand," said BBC head of news James Harding at the time.
When people first use BBC+, it asks them to choose at least three topics from a list of more than 50 options.
Examples include:
The app then creates a scrollable "at a glance" feed and the option to click through to specific themed pages.
Once the user has flicked through all the options, they are presented with a page saying: "You're up to date!".
At present, the app appears low down in Apple's App Store and Google Play when searched for, but over time this should improve.
Many users had already signed up to have a myBBC account ahead of the new app's launch.
The feature allows the broadcaster to target its content and make it a smoother experience for users to move from one device to another while using its services.
Having an account is optional on some apps, such as BBC News, but obligatory on others, including BBC Music and BBC Bitesize.
"As seven million people have signed up to myBBC, we are increasingly able to provide them with more of what they love based on what they've told us," said Paul Owen, head of BBC+.
"BBC+ is a key part of the journey towards achieving a much more personal BBC, and truly brings topical information from across the whole organisation to your pocket, ready for you to access at your convenience."
The BBC has promised not to sell the data it gathers and allows users to delete information held about them.
But Mr Pescatore said gathering the data would give the BBC a competitive advantage.
"There is a huge vested interest for the BBC to get consumers signed up with a BBC ID," he said.
"If this app helps get people on board it will be yet another threat to other news outlets and broadcasters."
The BBC has launched a new app that presents a selection of the broadcaster's online content chosen to appeal to each user's interests.