Just was thinking this morning. Wondering if there were any specific cases, if there were a lot of soldiers doing this, or if they were not able to.
Sure. For example Erich Hartmann, Gerhard Barkhorn and Günther Rall (the top three German fighter aces in WW2) would all eventually rejoin the west German air force (Bundesluftwaffe).
Yes, in fact one of the commander in chief of NATO was a wartime Wehrmacht general!
General Hans Speidel was an officer of the Wehrmacht who fought on the eastern front, he was later a member of the July 20th conspiracy to assassinate Hitler. He was one of the few to escape detection following the failure of the plot, and the military panel which interrogated him was convinced of his innocence. He was involved in the creation of the Bundeswehr after the war and was appointed CiC of NATO forces in Europe from 1957 to 1963.
Minoru Genda was one of the chief planners of the Pearl Harbor attack and postwar rose to became the chief of staff for the Japanese Air Self-Defense Force.
In the case of the Federal Republic, the general silent compact for ex-Wehrmacht veterans was that you were allowed to serve so long as you shut your mouth about the Third Reich and followed the loose denazification policies. The prevailing logic of using these veterans was that the professionalism and experience of these men would also give the new units a sense of tradition, albeit one allegedly scrounged of any taints of the Third Reich.
Of course, some of veterans could not abide by this like Hans Rudel, who became active in far right circles and would periodically extol Hitler. This led to what has been termed the Rudel-Affäre (Rudel Scandal) in which Rudel was invited to a veteran's meeting held on a current airbase. Several Bundeswehr generals were in attendance, including the aces Krupinski and Franke and they were on record congratulating Rudel as a true patriot. This prompted a degree of hand-wringing in the Defense Ministry and the cashiering of Krupinski. This also led to a general house-cleaning within the Bundeswehr to eliminate the vestiges of traditionalism within the West German armed forces and attempt to reorient the military ethos towards a more civic military.
Sources
Abenheim, Donald. Reforging the Iron Cross: The Search for Tradition in the West German Armed Forces. Princeton, N.J.: Princeton University Press, 1988.
_. Image of the Wehrmacht in Federal German Society and in the Tradition of the Bundeswehr. Monterey, Calif: Naval Postgraduate School, 1999.