The transaction will be completed in the next few days.
When the dairy company first announced the deal last August it expected to spend $615 million on an up to 20 per cent stake, but currency movements since then have increased the purchase price.
Fonterra hopes a distribution deal that comes with the shareholding 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.
The partnership is expected to give Anmum access to about 80,000 retail outlets in the world's second-biggest economy.
Paravicini said the tender offer's completion meant Fonterra could now finalise the distribution agreement with Beingmate.
"For sure it will be in the remainder of this year that we will see a key uplift [in Chinese Anmum sales]."
Beingmate, however, is facing its own issues in China's complex and highly competitive infant formula market.
According to a preliminary result released last month, annual profit fell 91 per cent to 65.7 million yuan ($14.3 million) as costs increased and revenue fell.
Fonterra had conducted thorough due diligence on Beingmate and had not been surprised by the profit decline, Paravicini said.
He said the company was happy with the shareholding it had secured.
"We are extremely satisfied and confident that the partnership can and should proceed on the basis of the 18.8 per cent stake," Paravicini said. "It is a good result."
Through the partnership a joint-venture arrangement for ownership of Fonterra's Darnum manufacturing plant in Australia is also planned, with Beingmate set to acquire a 51 per cent stake in the factory.
The joint venture, which was subject to Australian regulatory approvals, would be up and running by the second half of this year, Paravicini said.
He said Fonterra had not seen any impact on Chinese sales or market access as a result of last week's announcement of an anonymous threat to poison New Zealand infant formula with 1080 pesticide.
Beingmate shares closed at 17.68 yuan on Friday, just below the 18 yuan a share price Fonterra paid for its stake.
Units in the Fonterra Shareholders' Fund closed up 6c at $5.89 last night.