 The first white settlers to occupy the site of Madison were a party led by Henry Mitchell Barnes , who settled near the junction of Union and Taylor Creeks in 1867 . Growth of the new settlement was rapid ; in particular , there was an influx of German families from Wisconsin . The town of Madison was officially <unk> by Barnes in 1870 or 1871 . In 1875 , it became the county seat of Madison County , and in 1876 it was incorporated . The Union Pacific Railroad reached Madison in 1879 ; by 1880 , the town had a population of about 300 . 
