The two companies now intend to complete the transaction within the next two weeks - forming a 50:50 joint venture that will be known as Vodafone Hutchison Australia (VHA).
The merger was approved despite the Australian Competition and Consumer Commission citing initial reservations about what the proposed deal would mean for competition in the mobile telecommunications market.
After three months of investigations, the regulator now says such a merger "is unlikely to substantially lessen competition."
"The ACCC considered evidence which showed that absent the merger, the parties are unlikely to sustain the significant investment in their mobile networks to provide competitive high speed data services, such as mobile broadband," the regulator said in a statement.
Shareholders approved the merger in early April.
Nigel Dews, CEO of Hutchison Telecoms and proposed CEO of VHA, said: "Our first priority is to retain the best elements of both independent brands. The next step is to apply the combined scale and resources of VHA to deliver real benefits to all customers."
The two companies will maintain the Vodafone and 3 brands, their respective network arrangements, caps and plans, retail outlets and customer service capabilities "for the foreseeable future," a statement from Vodafone said.
Ovum analyst Nathan Burley said the decision was "in the best interests of the industry and consumers."
"Our view always has been the ACCC should allow this merger to go through," he told iTnews. "In the long-term, the Australian marketplace can't support four national mobile infrastructure players."
Burley said there is "no way" four national mobile operators would see the value in all making an investment in new mobile networks based on LTE (Long Term Evolution) or "4G" technologies.
"It's just not going to happen," he said. "For years financial analysts have talked about who might consolidate with whom to bring the number to three, a number that is sustainable in the long-term."
Burley shrugged off the ACCC's initial concerns that the merger would reduce Hutchison's 'disruptive and price-aggressive' effect on the market.
"It would have been interesting to see what Vodafone and Hutchison would do if the deal hadn't been approved," he said. "If the ACCC punishes Hutchison for being too aggressive, it's ridiculous. Where does Hutchison go from there?"
Burley said the last-minute promise that VHA will maintain prices for two years is meaningless.
"Prices always go down in telecoms, be it voice or data," he said. "Around the office we saw the price guarantee as a signal that VHA has already done a deal with ACCC."
Burley expects conditions were attached. "Something like a guarantee of x, or a sell-off of y assets. That sort of thing."
But the ACCC insists the price guarantee had no bearing on it's decision. "Behavioural measures, such as this, are generally viewed by the ACCC as an unattractive merger remedy," said ACCC chairman Graeme Samuel.
"Such measures are not likely to be considered acceptable by the ACCC to assuage competition concerns."