German Prisoners of War held in the continental United States were repatriated to Europe, a few in 1945 and the larger portion in early 1946. They were not necessarily repatriated as free men however, but were used as labor battalions in France, other occupied countries, and the American occupied zone in Germany. They were employed rebuilding damaged infrastructure, and in agriculture and coal mines to alleviate Europe's postwar food, fuel, and heating shortages. France's treatment of POW labor was initially so substandard that Eisenhower halted transfers but improved enough to resume them in November 1945. For many men, this term of labor was about 3 to 6 months, although the American occupation did not officially release the last POW laborers until June 1947. France still had 440,000 prisoners in April 1947, when it was pressured by the US to accelerate it's release and repatriation program, and a few were retained into 1948 as salaried workers.

The slow release of prisoners was in part designed to make sure the occupation of Germany was stable. A large release of unemployed men with military training was feared as likely to spark political violence. However the use of prisoner labor was in part punitive, and some former POWs were used in tasks like clearing minefields.

As far as I am aware, prisoners were released into the occupied zone (American, French, or British) controlled by the nation which had custody of them. In the American zone, they then received a free train ticket and interzonal pass from the prisoner discharge center to their home, assuming it was in one of the three western zones. If any former POW wished to head into the Soviet Occupied zone, this was not permitted after the border was blocked in mid 1946. I haven't seen any source claiming U.S. held POWs were forced into the Soviet zone.

Source: Krammer, Arnold "Nazi Prisoners of War in America"