Klepper was born in Beuthen an der Oder , Silesia, the son of a Lutheran minister. He originally studied theology at the University of Breslau, but dropped out to become a radio journalist in Berlin before being ostracized by the Nazi Party for his marriage to Johanna Stein, a Jewish widow with two daughters. He was fired from his work with Berliner Funk in June 1933, and was later fired from Ullstein Publishing House in September 1935. He had written favourably about a Prussian king and the stark differences to the current government. The book became very popular and by March 1937, he had lost his license to publish his largely Christian works from the state literary office. He appealed this with a letter to Joseph Goebbels, signing his protest with a Heil Hitler, and the case was ceded.

In December 1940, he was drafted by the German Army ... perhaps a bureaucratic mistake since citizens married to Jews were not to be drafted. His wife however had been baptized and they had a church wedding ceremony in 1938. While Klepper did not see combat, he served in a supply unit for forces through Bulgaria, Poland and Russia before being discharged in 1942 to tend to his wife.

On December 11, 1942, after Adolf Eichmann refused a visa for the couple's second daughter, the three of them committed suicide by turning on a gas valve - Jochen writing in his journal just before they died: Tonight we die together. Over us stands in the last moments the image of the blessed Christ who surrounds us. With this view we end our lives. After their death, the diary was given by Jochen's sister Hildegard, to the Allied trial against Adolf Eichmann where it was used as evidence against him (Session 51).

The book "In the Shadow of Your Wings", appeared in 1956, contains a selection from the diaries of Klepper.

Klepper wrote many church songs and they are used in today's evangelical song books.