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I have some DEM files that use a coordinate system that doesn't align well with WGS84. I can align them through the data frame properties -> Coordinate Systems Transformation, where i type Only the x,y,z correction in meters.

I want to make this transformation permanent (create a new DEM file that aligns well with WGS84) but dont seem to find a tool to do this like i do in the data frame properties (by using the 2 coordinate systems and the x,y,z correction in meters).

Any ideas?

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If your DEMs are not in a Projected coordinate system, first reproject them to something that makes sense for your project area (e.g., appropriate UTM zone).

Then, go to the layer properties in Catalog > XY Coordinate System. Right click on the Projected Coordinate System you are now (or were already) using and click Copy and Modify. Rename it to something like UTM_Custom and change the False Easting and False Northing to put your shapefile where you need it to be. Making the False Easting value larger moves the layer west. Making the False Easting value smaller moves the layer east. Similarly, making the False Northing larger moves the data south. Making the False Northing smaller moves the data north.

Click OK, then add the new custom projection to your Favorites so you can find it again later.

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After the custom transformation is set up, right-click the layer and select data > export data. In that dialog, choose to use the data frame's coordinate system.

Fill out the rest of the dialog and once you click OK, it will create a new dataset in the data frame's coordinate system.

An alternative solution is to use the Create Custom Geographic Transformation tool. This will persist the custom transformation. Once that's created, you can use the Project Raster Tool to create a WGS84 version of your data.

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If you want to make your DEM "align well" with WGS84 you can use the Project tool. From the linked webpage:

Projects spatial data from one coordinate system to another.

Usage: If the input feature class or dataset has an unknown or unspecified coordinate system, you can specify the input dataset's coordinate system with the Input Coordinate System parameter. This allows you to specify the data's coordinate system without having to modify the input data (which may not be possible if the input is a read-only format). Also, you can use the Define Projection tool to permanently assign a coordinate system to the dataset.

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