Police said the 39-year-old turned up at the local police station with his wife on Thursday. Police officers then accompanied the couple to a house in Råholt, south-eastern Norway.
In the adjoining garage, police found a Citroen Berlingo van with extensive damage to the front windscreen and the right-hand side of the vehicle. Police on Wednesday said they were looking for a van that matched this description.
The house where the van was found is occupied by the suspect's parents.
The 39-year-old has now been charged with manslaughter, police said. If found guilty, he could be jailed for up to three years, or up to six years under aggravating circumstances.
At a press conference on Thursday afternoon, police said they remained unsure whether the suspect was the person behind the wheel at the time of the collision. An investigation is ongoing.
Jeff Mwangi Kwirikia died from his injuries after he was run over by a van on county road 454. The driver fled the scene.
The van was last seen headed in a northbound direction on the stretch of the Trondheim road between Dal and Råholt shortly after the accident at 2pm on Tuesday.
The victim's daughter, Stella Mwangi, 25, represented Norway at the Eurovision Song Contest in 2011.
She also recently appeared on television with her father in the Norwegian version of Let’s Dance, in which she was a participant.
“She’s not doing well at all. Stella was very close to her father. She is mainly mourning her loss, not hunting for the driver,” her future father-in-law, Per Rogstad, told newspaper Romerikes Blad.