The books constituted the inaugural Statham Prize, an award given to a deserving Otago Boys' High School pupil.
The first recipient, in 1917, was David Faigan, Mr Faigan's father, and the volumes remain a treasured family heirloom.
Mrs Hobson was Frank and Clive's older sister. She endowed the prize to honour the men, who were killed by the same Turkish shell when standing standing side by side near the summit of Chunuk Bair on August 9, 1915.
The Stathams' father was prominent Anglican churchman Charles Statham; their older brother, also Charles, was already on the Dunedin City Council and would eventually become an MP and Speaker of the House of Representatives.
''Frank and Clive are well remembered by their family,'' Janet Statham, Frank's Sydney-based granddaughter, said.
''I have been to Gallipoli three times, the first in 1974 and the most recently in August 2015, when I stood on the spot where Frank and Clive were killed.''
There is a stained glass window dedicated to them in St Paul's Cathedral in the Octagon, and the brothers' names are on the memorial archway at the entrance to Otago Boys', which both attended.
This year's Anzac Day address at the school will be on the Statham brothers.
''I am a very proud granddaughter of Frank, and I am delighted that Otago Boys' High continues to recognise the contribution some of its students made in World War 1,'' Ms Statham said.
Mr Faigan has spent most of the last 50 years overseas, but was delighted to return the first Statham Prize to the city.
''This item of great local interest is now returned to Dunedin for this first time since my father moved to Auckland in the late 1920s where he married and raised his family,'' he said.
''It is my intention to eventually leave the books, letter and photograph to the Rare Book Collection of the Dunedin Public Library.''
