  The LEGEND experiment, now under construction, will operate a large array of
Ge detectors for the search of neutrinoless double-beta decay of $^{76}$Ge. In
this paper we report on the process development for the hydrogen reduction of
germanium dioxide enriched in $^{76}$Ge as part of the effort to manufacture
detectors for the LEGEND experiment. The process was optimized via a kinetic
un-reacted shrinking model and tested with a batch of natural GeO$_2$. We
completed the reduction of a batch of 23 kg isotopically enriched Ge with an
average yield of 99.85%. Subsequently, the Ge was purified to intrinsic purity
by zone-refining and an overall Ge yield of 99.05% was achieved. Using an
intermediate underground storage, an average cosmogenic exposure of 156 h was
accumulated. Special care was taken to avoid and recycle losses during the
process.
