The extensions were announced on Friday, just a week after Germany booked their place at next summer's World Cup finals.
"I really enjoy working with the team and the coaches and I feel a great deal of motivation to develop this team further," Low told the German Football Association's official website.
"We're not yet at the end of our path and we still have big goals that we want to achieve together."
Low took over as Germany coach following the 2006 World Cup, replacing Jurgen Klinsmann, for whom he had worked as assistant.
"The DFB (German Football Association) give us and the national team ideal surroundings to work in, for which we are as grateful as we are for the trust the DFB and president Wolfgang Niersbach have in us," continued Low, who will lose his assistant Hans-Dieter Flick after next summer's World Cup.
Flick will take on the position of the DFB's director of sport from next summer, having signed a five-year contract on Friday.
"For Jogi Low and myself, the World Cup in Brazil is our absolute priority," Flick said.
"It honours me and delights me that the DFB trust me with this varied and responsible role as director of sport after the World Cup in Brazil while at the same time giving me the liberty to concentrate fully on the World Cup up until then.
"As director of sport, I will then dedicate myself to ensuring that Germany's best footballers also have the best surroundings in order that they can develop.
"Only then can we demand world class performances, and that has got to be the DFB's goal."