"I'm very happy to continue working with the DFB (German federation) and the team," Low, who led Germany to third place at the World Cup in South Africa and had been briefly out of contract since then, told reporters.
"We had a great time with the team at the World Cup and are looking forward to the next challenges. We have great motivation to lead and develop this team further."
Germany went into the World Cup under a cloud and missing injured captain Michael Ballack.
However, they flourished despite Ballack's absence, scoring four goals apiece in wins over old rivals England and Argentina on their way to the semi-finals where they were beaten 1-0 by Spain.
Low would not be drawn on the captaincy row which has blown up since the World Cup between Ballack and Philipp Lahm, who wore the armband in South Africa.
"I have not made up my mind on this, it's important for me to speak to the players and let them know my decision personally," he said.
Lahm said in an interview during the World Cup that he would not give up the captain's armband of his own free will, a comment which has annoyed Ballack.
Last week, Ballack hit back, saying he still considered himself to be captain and that Lahm's remarks had irritated him.
Low, 50, was assistant to Jurgen Klinsmann for two years and took over as senior coach when Klinsmann decided not to renew his contract after the 2006 World Cup.
He led Germany to the final of Euro 2008, where they also lost 1-0 to Spain.
Low had previously failed to renew his contract last February, leading to suggestions of a rift between himself and the DFB.
But DFB president Theo Zwanziger said Tuesday: "It has always been my personal goal to extend the contract with Joachim Low and his team."
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