Before 20th June 1948, both the Rentenmark and the Reichsmark were the legal tender of Germany (as they had been since 1923 and 1924 respectively). However, it was on this day that a new currency (the Deutsche Mark) was introduced in the newly formed West Germany.

Because of this currency reform in West Germany, there was an obvious implication: the currency in West Berlin had also been changed. Combined with the fact that, at this point in time, people were still moving freely between East and West Berlin, this currency reform in the West had huge economic repurcussions in the East (and was one of the reasons why the infamous Berlin Blockade happened). The problem was that East Berlin still used the old currency. This meant that all the (now worthless) Rentenmark and Reichsmarks from West Berlin flooded the Soviet occupation zone, causing massive inflation. This sparked the Soviets into eventually doing what had already been proposed: changing the currency of East Berlin. This new currency was introduced on 24th July 1948, and was also called the Deutsche Mark, however in the West it was known as the Ostmark or East Mark.

TL;DR: June 1948 in West Germany, and 24th July 1948 in East Germany.

Sources:

http://www.bbc.co.uk/schools/gcsebitesize/history/mwh/ir2/berlinblockaderev1.shtml

http://en.wikipedia.org/wiki/Deutsche_Mark#Currency_reform_of_June_1948

http://en.wikipedia.org/wiki/East_German_mark#1948

Also, I just finished studying this at university.

Edit: missed out the day the Deutsche Mark was introduced in West Germany.