Time machine backup won't integrate with my newly migrated mac.

I migrated from my old computer to my new one, mac to mac, using the migration assistant. Now when time machine comes to do a backup of my new mac it thinks that all of the original backup has changed and tries to copy all of my files on my new mac to the backup, duplicating everything.

Is there someway to make time machine recognise all of the files on my new mac as the files it has backed up?

Thanks.