Authorities said late on Monday the collision occurred at an altitude of 2500 metres. They initially thought it took place at a higher altitude of between 3 and 5 kilometres.
One of the engines of the civilian jet was sheared off in the impact and crashed on a road, the official said.
The rest of the aircraft came down in a wooded area near Olsberg-Elpe in North Rhine Westphalia, missing a house by about 90 metres.
Officials confirmed the death of only one of two people on board the Lear jet. The aircraft went up in flames when it crashed in a forested area in the Sauerland region, the police spokewoman said.
The occupants were identified by police only as a 50-year-old and a 43-year-old from Schleswig-Holstein.
The mid-air collision occurred while the Eurofighter jet was participating in a joint exercise with another Eurofighter.
A full fuel tank was torn off in the collision, but the jet was able to land safely at a military base in Noervenich near Cologne, Colonel Andreas Hoppe said.
Both of the aircraft were struck on the wing and fuselage, he said.
The crash site was hard to access, but body parts were found near the crash site, a police spokesman in Meschede said.
The Lear jet belonged to a subsidiary of Airbus Defence and Space that is contracted to assist the German military on its manoeuvres.
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