The software, called Cider, has been created by postgraduate researchers at Columbia University.
Cider lets Android gadget owners mix and match the Android and iOS apps they load on their phone or tablet.
The research team said Cider was only a prototype and that they had no plans to turn it into a commercial product.
The six-strong team of researchers said they embarked on the project to create Cider to get around the limitations that smartphone and tablet users are forced to accept.
For instance, they said in an academic paper about Cider that Android users cannot get at apps that call on media in Apple iTunes and iOS gadget owners struggle to use Flash-based content.
Cider would let people use just one gadget to access both, said the researchers.
Getting an application written for one operating system to run on another often involves a technique known as virtualisation.
To avoid the performance problems that virtualisation can introduce, the Columbia researchers adopted a different approach that involves the core or kernel of the Android operating system.
This approach works on the stream of instructions passing through an Android device and alters only those relating to the iOS apps. An additional software helper provides some of the specialised data those apps require to work properly.
A demo video produced by the researchers shows both iOS and Android apps running on a Nexus 7 tablet, though some commentators pointed out that the Apple apps run relatively slowly on the device.
In addition, some Apple apps that call on a phone’s camera, GPS system or Bluetooth perform poorly and the researchers are continuing their work on Cider to fix these problems.