A series of memorial events would begin in 2014, with the centenary of the Gallipoli landing in 2015.
More than 10,000 New Zealanders and Australians were expected to make the pilgrimage to Turkey for the 2015 memorial, prompting Government to consider a ballot system for travel to the tiny peninsula.
The Ministry of Culture and Heritage has proposed running a series of events between 2014-18, including a heritage trail and restoration of war memorials.
Mr Tremain said the $200 million in lottery profits from Lotto, Instant Kiwi and Daily Keno proceeds was $26 million more than forecast.
Sport New Zealand received $34.6 million of the lottery proceeds, Creative New Zealand received $26 million, and the New Zealand Film Commission $12.1 million.
Lottery grants:
$27.48 million - new World War One Commemorations, Environment and Heritage Committee (at least $17 million for WWI activities)
$25.95 million - Creative New Zealand
$12.1 million - NZ Film Commission (including NZ Film Archive)
$34.6 million - Sport New Zealand