Melle studied law at the
Georgia Augusta University in
Göttingen and became a lawyer in Hamburg in 1876, also writing articles for the newspaper
Hamburgischer Correspondent. In 1886, he became a full-time journalist with ''''. In 1891 he joined the executive board of Hamburg's senior school authority (Oberschulbehörde) and was appointed syndic attorney of the city-state of Hamburg. In 1900 the Hamburg Parliament elected Melle as fellow senator into the
Senate of Hamburg, the executive government of the city-state. Although elected for a life-term, he remained senator only until 1921. For the calendar years 1914 and 1917 the fellow senators elected him deputy mayor (Second Mayor of Hamburg). Then the fellow senators elected him
First Mayor of Hamburg, thus head of state and of government (president of the senate) – though under the auspices of a
primus inter pares regulation – for the full calendar years 1915, 1918 and for the term 31 March to 31 December 1919. On 12 November 1918 the
Hamburg revolutionary Soldiers' and Workers' Council deposed the Senate of Hamburg, but reappointed the senators as acting administration only on 18 November. In this function Melle continued as acting First Mayor beyond his election term, actually ending on 31 December 1918, until the complete senate resigned on 27 March 1919, thus ending the life-term mandates under the old 1860 constitution. On 30 March 1919 the Hamburg Parliament, first time elected under equal suffrage by men and women of Hamburg, elected a new senate, into which Melle and six more pre-war senators were reëlected, besides eleven new senators. On 31 March 1919 the fellow senators elected Melle again their president and First Mayor of Hamburg. His predecessor as First Mayor was
Max Predöhl (in 1914 and in 1917), his successors were
Carl August Schröder in 1916 and
Friedrich Sthamer in 1920. ==Awards and honors==