Arla said it had paid 71 pence per share to buy the 49 per cent stake it did not already own in its UK arm, valuing the company at £434m.
The deal enables Arla to have more say in the UK, which now accounts for a third of the dairy giant's sales revenue and where it is one of the top three dairy firms.
Investors appeared to back the deal, with Arla UK's shares at 69.5 pence Tuesday morning. The company's share price has risen substantially since buyout talks were announced in the autumn.
Peder Tuborgh, Arla Foods chief executive, said: "Outright ownership will ensure that the business of Arla Foods UK derives the full benefits of being part of the largest dairy business in Europe and will enable us to strengthen the relationship with UK dairy farmers."
His comments suggest Arla Foods may look to take a more hands-on approach in the UK.
The takeover follows earnings problems at Arla UK, despite strong branded sales thanks to products such as Lurpak butter and Cravendale milk.
Arla Foods warned the UK team last year that a £0.9m loss in the six months up to 31 March had been unsatisfactory.
"We are proactively working with and encouraging Arla UK's management to develop and implement plans to deliver long-term improved performance," the Scandinavian parent firm said.