The 3m high (10ft) objects arrived at the site in Wakefield, West Yorkshire, following a tour of Europe, Asia and the US.
The heads are inspired by traditional Chinese zodiac statues which once decorated a fountain clock at an imperial palace retreat in Beijing.
His interpretation is part of the park's 40th anniversary celebrations.
Each sculpture in Circle of Animals/Zodiac Heads (2010) is cast in bronze and weighs 363kg.
The artist said he wanted the work to be playful and accessible to the general public.
"I want this to be seen as an object that doesn't have a monumental quality, but rather is a funny piece," he said.
"People can relate to or interpret on many different levels, because everybody has a zodiac connection."
The palace which housed the original zodiac heads -  Yuanming Yuan - was ransacked in 1860 by the British and French.
Since then only seven of the heads have been returned to China - the rat, ox, tiger, rabbit, horse, monkey, and boar.
The other five - dragon, snake, goat, rooster, and dog - have yet to be found.
Weiwei's latest work joins his Iron Tree (2013) sculpture at the park, which has been in the Chapel courtyard since 2014.
It also forms part of a series of projects developed by the park investigating migration and human freedom, which includes Shirin Neshat (2011), Yinka Shonibare (2013), Amar Kanwar (2013) and Beyond Boundaries: Art by Email (2017).
Twelve bronze animal head sculptures by Chinese artist Ai Weiwei are on display at the Yorkshire Sculpture Park.