Jeschke was born in 1936 in Děčín (then in Czechoslovakia, now in the Czech Republic). After the expulsion of Germans from Czechoslovakia after World War II, he grew up in Asperg near Ludwigsburg. After graduating from high school, he trained as a toolmaker and worked in mechanical engineering. In 1959, he went back to complete the and studied German, English literature, and philosophy at Ludwig Maximilian University of Munich. He completed a publishing internship at the publisher C.H. Beck. In 1969, he was hired as editorial assistant for the Kindler literature encyclopedia, and later became an editor.