ANZAC Day is not "celebrated": it is commemorated.
The original ANZAC landing at Gallipoli occurred on 25 April 1915. From 1916 onwards, in both Australia and New Zealand, ANZAC services were held on or about April 25, mainly organised by returned servicemen and school children in cooperation with local authorities.
25 April 1916 was the first unofficial ANZAC day. It was marked by a wide variety of ceremonies and services in Australia, a march through London, and a sports day in the Australian camp in Egypt. In London over 2,000 Australian and New Zealand troops marched through the streets. In the Sydney march wounded soldiers attended by nurses also took part in the march with the aid of motor vehicles.
ANZAC Day was gazetted as a public holiday in New Zealand in 1921. In Australia, it was decided at the 1921 state premiers conference that ANZAC Day be observed on April 25 each year. Initially, it was not observed uniformly in all the states.
It wasn't until 1927 that all Australians commemorated the day with a public holiday.