Eimer was born in Stäfa, Switzerland where his father, who had taken refuge following an attempted coup against the German Confederation in Frankfurt in 1833, practiced medicine.

After studying at gymnasiums in Bruchsal and Freiburg where his father worked, Eimer matriculated at Tübingen, where he was influenced by Franz von Leydig.

He spent the winter semester of 1865 at the University of Tübingen and in 1866 he worked in Berlin at Rudolf Virchow’s laboratory.

Eimer made use of studies (based possibly on the suggestion of Kölliker) that he conducted on a blue variant of the Italian wall lizard (Podarcis siculus coeruleus) found on the Faraglioni Rocks off Capri.

He explained that the island had little vegetation which made them blue rather than green which he claimed was closer to the colour of the rocks and therefore adaptive but he did not explicitly invoke selection as a process.

Though his theories gained popularity in Germany in the 1880s, his work was not widely known in the English-speaking world until 1890 when his work Die Entstehung der Arten auf Grund von Vererben erworbener Eigenschaften nach den Gesetzen organischen Waschsens (1888) was translated by Joseph Thomas Cunningham as Organic Evolution as the Result of the inheritance of Acquired Characters according to the Laws of Organic Growth.

Eimer's later work, translated as On Orthogenesis, was a more rigidly orthogenetic text, whereas Organic Evolution maintained a plurality of mechanisms for species formation.