Mr Andrew is a fifth generation South Sea Islander, as the Australian descendants of Pacific island plantation workers are known.
They were kidnapped or recruited in the 19th century to labour on Queensland's sugarcane plantations.
The Queensland MP was accompanied by the Queensland Speaker of Parliament, Curtis Pitt.
The Daily Post reported Mr Andrew, who has relatives on the island of Ambae, was given a custom welcome by Ambaean chiefs when he arrived in Port Vila.
The delegation is expected to travel to Ambae where the MP will be given a chiefly name.