Fonterra hopes the deal will help its Anmum infant formula brand, which was launched in China in 2013, gain traction in the Asian superpower's booming baby-milk market, which the company has projected to almost double in size, to $33 billion, by 2017.
Chief financial officer Lukas Paravicini said both companies had made a provision for the tender offer possibly reaching less than 20 per cent.
"Our goal was to acquire up to 20 per cent," he said.
"We are extremely satisfied and confident that the partnership can and should proceed on the basis of the 18.8 per cent stake. It is a good result.
"Over the next few weeks, Fonterra and Beingmate will now move ahead with the next phase of our partnership, which includes establishing a joint venture to purchase the Darnum plant in Australia and finalising a distribution agreement making Beingmate Fonterra's exclusive Anmum distributor in mainland China."
Beingmate reported a 90 per cent drop in annual profit to 65.7 million RMB ($14.3 million) last month.
Beingmate shares, which closed at 17.68 yuan ($3.85) on Friday, have gained 9.2 per cent this year.
Meanwhile, a Fonterra spokesman said on Friday that the company had not had any products held up at the Chinese border as a result of new import certification requirements introduced following the 1080 threat, which was made public last week.
One small-scale exporter said he had $1.5 million to $2 million worth of infant formula stuck a port in Shanghai because it did not have a "1080-free" certificate.
The co-operative and Federated Farmers received letters from an anonymous activist in November threatening to poison infant formula with the pesticide.
The spokesman said the threat had had no impact on Fonterra's sales or orders last week.
