Photo stream and iCloud?
One way i can think of is using a Mac:


Sync your old iPhone and download your photos to iPhoto.
Activate iCloud and Photo Stream on your mac using your iCloud ID.
iPhoto now will have a Photo Stream folder.
Drag the desired photos/events to the Photo Stream folder in iPhoto.
Make sure you have Photo Stream activated on your iPhone 4S and you are using the same iCloud ID on all related devices.
iCloud on your iPhone 4S should detect via WiFi or your carrier that you have photos in your Photo Stream and will sync all devices under your iCloud ID.


I haven't managed to copy the photos to the Photo Stream Folder on the phone, so maybe it's not implemented yet, but one workaround if you don't have a Mac, is to email/message yourself the photos. Read the mail/message using your new iPhone 4S and save the photos. They will appear in the Photo Stream folder.

Hope that helps.