Former Koevoet member Leon Lotz, of KwaZulu-Natal, is among scores of former South African security force personnel helping to train government and allied forces to fight the insurgents.
The group of which Lotz was a member is believed to be contracted to the Nigerian government. It does not have the support of the South African government.
Lotz and five others, including another foreigner and four Nigerian soldiers, were killed on Monday near Maiduguri.
The nationality of the other foreigner is not known.
Maiduguri, the capital of Nigeria's north-eastern Borno state, has been the scene of intense fighting between Boko Haram and pro-government militias fighting alongside government troops.
About 80 South Africans are providing assistance to the forces engaging Boko Haram in the form of advice on military tactics and intelligence gathering, and training in the use of heavy weapons and advanced fighting techniques.
Lotz's neice, Vanes-Mari du Toit, posted on Facebook: "What an absolute honour knowing you. You fought for what was right, always had the best advice.
"Today I say goodbye to a legend of an uncle, who passed away in battle fighting Boko Haram ... Rus sag, Oom (Rest softly, Uncle)."