"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."
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.
"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.
But DFB president Theo Zwanziger said Tuesday: "It has always been my personal goal to extend the contract with Joachim Low and his team."
