VW, which was obliged by German law to make a public offer for MAN shares after its holding rose recently above 30 percent, was "more than pleased with the result," a statement quoted chief executive Martin Winterkorn as saying.
The group has acquired 53.7 percent of the capital and 55.9 percent of the voting rights in MAN, paving the way for a tie-up with Scania of Sweden, which VW also owns.
It wants to merge the two truck makers along with its own heavy vehicle activities to create a rival for two other European heavyweights, Daimler Trucks and Volvo Trucks.
Regulatory approval for various parts of VW's plans must still be obtained however, and the group plans to begin by working for 200 million euros ($290 million) in cost savings through joint purchases for the different brands.
VW had offered 95.00 euros ($138.51) for ordinary shares and 59.90 euros for preference shares in MAN, which also makes diesel engines and industrial turbines.
According to an AFP calculation, VW thus paid a little more than 3.4 billion euros for 35,857,607 of the former and 164,613 of the latter.
"Our objective of realising substantial synergies between MAN, Scania and Volkswagen in the interest of all shareholders, employees and customers is moving closer," Winterkorn said.
VW would now work quickly to obtain necessary global regulator approvals for "a closer cooperation" of the truck makers, the statement added.
The automaker owns 70.94 percent of the voting rights in Scania, while MAN owns another 17.4 percent.
VW had initially sought only 35-40 percent of MAN's equity to provide it with a decisive vote during shareholder general assemblies.
But a MAN spokesman told AFP: " Our shareholders have decided, MAN will belong to the VW family. We are opening a new chapter in MAN's long history."
MAN, which was founded 253 years ago as a steel company, plans to "take advantage of opportunities provided by this situation and fully support Volkswagen any way it can in examinations by European competition authorities," the spokesman said.
The European Commission has objected to VW naming three members of Scania's supervisory board to that of MAN, forcing a strategic retreat by Ferdinand Piech, who is head of the supervisory boards of both VW and MAN.
Shares in MAN showed a loss of 1.37 percent to 93.99 euros in midday trading on the Frankfurt stock exchange, while VW was up by 0.35 percent at 143.3 euros.
The DAX index on which they are listed was 0.11 percent higher overall.