He took his education at the Technical University of Munich, and opened an architect's office in Stavanger in 1881.
All these buildings are characterized by historicism, Neo-Renaissance architectural revival style, the latter with a different expression, performed mostly in raw red brick.
Eckhoff designed several villas in western Norway, and distinguished himself as a church architect.
His designs included Haukedalen church in Førde (1885), Bore in Klepp (1891), Skånevik ( 1900), and Ask (1908).
Besides his architect work, he was a teacher at Stavanger Cathedral School for thirty-three years.