After adding a new drive to my machine and re-installing Windows, the path of my custom-built Qt directory changed from
E:\Qt\4.8.3. CMake cannot use it in the new location, because it calls
qmake -query which returns the old paths which are hard-coded into the Qt binaries.
The solution is simple: create a qt.conf file in the same directory as the qmake binary containing:
[Paths] Prefix = E:/Qt/4.8.3
The corresponding Qt documentation page has more details.