Once you have populated the dialog with all of the assets you would like to use in the consolidation process, select one of the assets to serve as the "asset to consolidate to" and then click Consolidate Assets. All references to the assets you did not choose from the list will be replaced with references to the asset you did, deleting the non-chosen assets in the process.
The Consolidate Assets button is grayed out (and unavailable) until at least two assets are in the dialog and at least one is selected.
Inside the Replace References dialog, selecting an asset marks it as the "asset to consolidate to."
Upon clicking Consolidate Assets, you will be prompted with a Delete Assets dialog, which enables you to remove assets that are no longer referenced and thus no longer necessary. Click Delete.
All of the duplicates have been consolidated to the chosen asset!