The results come as the company's "dieselgate" crisis is back in the spotlight following the arrest this week of a VW executive in Miami who stands accused of helping to cover up the scandal. The scandal erupted in September 2015 when Volkswagen, under pressure from US authorities, admitted to installing software in 11 million diesel cars worldwide that could dupe pollution tests.
The cheating technology allowed the cars to pass the emissions tests but release up to 40 times the permitted amounts of nitrogen oxides during actual driving. The scandal harmed Volkswagen's reputation and sent its share price plunging, but customers appear to have largely shrugged off the controversy.
Volkswagen has responded to the crisis with a management shake-up and by shifting its focus to clean-energy vehicles, setting out to be the world's leader in electric cars by 2025.
"2016 was a very challenging year for us. We made strides in resolving and overcoming the diesel crisis and at the same time initiated a fundamental change process," chief executive Matthias Mueller said in a statement.
Group sales were driven by strong growth in China, where deliveries were up 12 percent. Europe saw growth of four percent. In the United States, where customers have taken mass legal action to secure compensation from Volkswagen, sales were down 2.8 percent over the year.
In South America, sales plummeted by nearly a quarter. Overall, VW's flagship own-brand cars were the group's most popular with sales up 2.8 percent to reach nearly six million units in 2016.
Strong performances by Skoda as well as luxury brands Porsche and Audi also helped drive the group to its record result.
Volkswagen's main global rival Toyota has yet to announce its full-year figures, but last month it said it expected sales of 10.09 million vehicles for 2016 - which would put it in second place behind VW.