Mr Koschnik said the timing of his resignation was purely personal. He had promised his wife he would step down when the time was right.
After last week's Rome summit on implementation of the Dayton peace accords, the city, divided between Muslims and Croats, was on the way to being unified again, he said. "This is, therefore, a good time for my successor to take up work."
Mr Koschnik said he would stay until the EU's mandate in the city expires in July, if it is difficult to find a replacement.
Despite Mr Koschnik's reassuring words, his departure caused concern among EU foreign ministers. Germany's Klaus Kinkel said he regretted Mr Koschnik was giving up his mandate. "He was and is the right man in the right place."
Mr Koschnik's success in maintaining a degree of stability in Mostar has been viewed as a litmus test of how well Bosnia's Muslim-Croat federation can succeed on a national scale.
Formerly mayor of Bremen, Mr Koschnik got the job after a US-brokered deal to halt Muslim-Croat fighting in March 1994. During his time in the city he has endured physical threats and mob violence. In 1994 an anti- tank shell exploded close to his bedroom.
Earlier this month his car was attacked by Croats as he announced his plan to reunify the city. Violence erupted again last week on the very day that Muslim and Croat citizens were to be allowed freedom of movement, as a first step to full reunification.
Mr Koschnik said yesterday he hoped his successor would have a more peaceful time.