The museum in south-east London officially handed over ownership of the artefacts to the Nigerian government on Monday.
The Horniman described returning the looted objects as a “moral and appropriate” response after a request from Nigeria’s National Commission for Museums and Monuments (NCMM).
The first six objects that are being returned, including two Benin Bronze plaques from the royal palace, were handed to Nigerian officials at a ceremony marking the transfer of ownership of 72 looted items.
The items were taken from Benin City by British troops in February 1897.
It is not clear whether thousands of items still being held at large institutions, including the British Museum, will ever be sent back.
Nick Merriman, chief executive of the Horniman Museum and Gardens, and Prof Abba Tijani, the NCMM’s director-general, were asked by journalists before the handover if they were frustrated at the British Museum’s apparent reluctance to hand over the 900 objects it has held for more than a century.
Mr Merriman said: “I would rather talk about what an excellent example the Horniman is rather than answer questions about the British Museum.”
The six objects form the first wave of physical repatriation of Benin objects from the Horniman. They include a brass hip ornament depicting a face or mask, an ivory staff of office depicting a carved relief figure and an ivory arm cuff carved with heads and abstract shapes, part of royal regalia.
The remainder will stay in the UK on loan, with a second phase of physical repatriations to follow.
Prof Tijani said he felt a “relief” at the Horniman’s return of the objects. He added that about 5,000 Benin Bronzes remained “scattered” around the world.
Frederick Horniman, the museum’s founder, bought the objects from Mr WJ Hider, of the Royal Navy, in March 1897. Mr. Hider accompanied the military incursion into Benin City and was personally involved in the looting, the museum said.