His father, Jens Pedersen (1802–1885) owned a farm; Jensen-Egeberg was born in Hedensted, Denmark, and grew up in the country.
He began his education at the Uldum Folk High School, near Vejle, then went to Copenhagen in 1865 to attend the Blågård Seminarium, but decided that he wanted to be a painter instead.
In pursuit of that, he took classes at the Copenhagen Technical College, received an award in 1874, and transferred to the Royal Danish Academy of Fine Arts.
His notable portraits include one of his parents (Old Folk, 1885), who both died shortly after it was exhibited, and one of his wife, which was shown in 1892.
The following year, he received public support for study trips, including a visit to Paris, and more exhibitions.