The Competition and Markets Authority said it has cleared the combination of the businesses, after finding that concerns raised over the deal did not warrant blocking it.
The deal is now set to be completed at the end of this month.
The Campaign for Real Ale had called for an investigation of the joint venture, saying it would reduce the choice of beers available to pubgoers.
The regulator said Marston's owns many pubs across the UK which might choose to serve more Carlsberg products, and fewer independent brands.
"The CMA found, however, that Marston's pubs form only a small part of the potential UK customer base for brewers, and that independent brewers would continue to have sufficient access to pubs after the merger, allowing them to compete effectively," it said in a statement.
The two companies want to create the Carlsberg Marston's Brewing Company, which would have its headquarters in Wolverhampton, with Marston's brewing business valued at £580m and Carlsberg's UK brewing division at £200m.
Marston's, which has pubs right across the region, said it will own a 40 per cent stake in the joint venture and will use the plans to focus on its pub and accommodation business.
A statement by Marstons said: "We are pleased to report that the Competition and Markets Authority have cleared the proposed joint venture, and the antitrust condition to completion has now been satisfied.
"The transaction will now complete at the end of October 2020."
Tomasz Blawat, managing director of Carlsberg UK, said: "We welcome the decision by the Competition and Markets Authority and wish to put on record our thanks to them for the thoroughness of their work in recent months.
“The joint venture between Carlsberg UK and Marston’s PLC to form the Carlsberg Marston’s Brewing Company, unites two historic brewers with shared values, history and heritage, to create a company with a sustainable future in UK brewing.
“Today’s decision is a significant milestone in the formation of the new company, which we believe will create significant value for employees, customers and beer-drinkers in the UK, and we look forward to moving to the next stage on this journey.”