CMA announced earlier today it has accepted "modified undertakings" proposed by Müller in June and approved the sale, which Müller and Dairy Crest expect to complete no later than December 27.
Under the deal, which was proposed in November 2014, and its bulk and potted cream and milk powder businesses for £80m.
It will also assume control of 72 depots, Dairy Crest's glass bottling site in Hanworth, and processing plants in Foston, Chadwell Heath and Severnside.
Ronald Kers, CEO, Theo Müller Group, said the company is “delighted we can now press on, drive towards completion of this transaction and begin work with our new colleagues to bring these businesses together.”
“There is no question that further consolidation is required in the UK fresh milk sector and with this hurdle now cleared, we have an exciting opportunity to create a more competitive, sustainable, efficient and innovative dairy processor in the UK,” Kers added.
Completion of the deal was delayed by an initial CMA assessment that concluded the transaction would give "rise to a realistic prospect of substantial lessening of competition in the supply of fresh milk" in the South West and Wales.
On June 12, CMA warned the proposed sale would be referred for an in-depth six month 'phase two' investigation unless "acceptable undertakings to address these competition concerns" were offered.
Two weeks later, it announced it was considering an offer by Müller to process a certain volume of fresh milk for a third party dairy processor in South West England and Wales.
Accepting the proposal in principle, it gave Müller until August 21 to "propose a named processor and draft arrangement to the CMA for approval."
Müller has addressed CMA's concerns with an agreement to contact process up to 100m litres of fresh milk a year for Medina Dairy at Severnside for between five and eight years.
"Medina Dairy's vision is to be a credible alternative supplier of liquid milk to the full spectrum of UK retailers, wholesalers and foodservice operators," said Sheazad Hussain, CEO, Medina Dairy.
"We are therefore delighted to have been chosen as the successful purchaser of the Severnside fresh milk processing volume following a very rigorous and highly competitive selection process satisfying the Competition and Markets Authority."
Dairy Crest has agreed to make a one-of payment of £15m to Müller on completion of the deal to help meet the additional cost of the "modified undertakings."
Mark Allen, CEO, Dairy Crest, heralded today's decision as “a transformational moment for Dairy Crest and the wider dairy industry.”
The sale - the proceeds of which will be used by Dairy Crest to reduce its net debt - will see the company focus on its successful cheese, butter and spreads businesses, which incorporate its Cathedral City, Davidstow, Clover, and Country Life brands.
Dairy Crest will also continue its project with Fonterra to produce and market demineralized whey and galacto-oligosaccharide (GOS) at its Davidstow plant in Cornwall.
“Dairy Crest will now be able to focus on growth,” Allen added, “through both our branded cheese and spreads operations and new revenue streams from manufacturing products for the fast-growing global infant formula market.”