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Go into the account section of the app (the logo looks like a business card) and select "set up a device"
Choose your new fitbit from the list. If it's the same model as your old fitbit then it will ask if you want to replace. If not it will add it to your account and you then need to select your old one and there will be an option to remove it.
All your data, settings, badges etc will be retained when doing this.