Yes, this is possible after you perform a system update on your Nintendo 3DS system.
To transfer your Nintendo DSiWare software to your Nintendo 3DS, you will need an Internet connection and your original Nintendo DSi Shop account will have to be intact. You will need access to both your original Nintendo DSi or Nintendo DSi XL system as well as the new Nintendo 3DS system.
Important: When transferring to a Nintendo 3DS system, all save data from any Nintendo DSiWare will be deleted. Once you have transferred Nintendo DSiWare from a Nintendo DSi system to a Nintendo 3DS system, you will not be able to move it back.
Please note that, as well as your Nintendo DSiWare titles, the system transfer will allow you to transfer Nintendo Wi-Fi Connection settings and data such as photos and sound recordings. When you transfer your Nintendo Wi-Fi Connection settings and photos and recordings, any such data already on your Nintendo 3DS system will be overwritten. If you wish to keep photos and recordings already on your Nintendo 3DS system, please move them to an SD Card before you begin the transfer. For more details, please see the eManual of the NINTENDO 3DS TRANSFER TOOL. To read the eManual, please tap the corresponding button in the application.
To start the process, please download the Nintendo DSiWare application NINTENDO 3DS TRANSFER TOOL on your Nintendo DSi or Nintendo DSi XL. You can find this in the Nintendo DSi Shop. Ensure that the battery on each system is well charged, or plug in the power supply before starting the transfer. Then follow these steps:
1. On the Nintendo 3DS system, tap System Settings, select OTHER SETTINGS, and then SYSTEM TRANSFER. Then touch TRANSFER FROM A NINTENDO DSi SYSTEM. Read the warning message about transferring data, then touch NEXT.
2. Touch RECEIVE FROM A NINTENDO DSi SYSTEM.
3. On the Nintendo DSi or Nintendo DSi XL system, open the NINTENDO 3DS TRANSFER TOOL from the Nintendo DSi Menu.
4. Touch TRANSFER TO NINTENDO 3DS. Read the warning message about transferring data, then touch NEXT.
5. Touch SEND FROM THIS SYSTEM.
6. Touch the user name of the target Nintendo 3DS system.
7. On the Nintendo 3DS system, touch YES to agree to the transfer.
8. On the Nintendo DSi or Nintendo DSi XL System, select FULL TRANSFER to move all transferable data or select CUSTOM TRANSFER to choose the items you want to transfer.