Low’s position came under threat after Germany suffered an embarrassing 6-0 defeat to Spain in the UEFA Nations League earlier this month.
That defeat cost Germany a place in next year’s UEFA Nations League finals and it was their heaviest loss for 89 years.
The decision means Low will remain in charge of Die Mannschaft for the rescheduled EURO 2020 next year.
"It was important for the national coach to discuss the current situation, the defeat against Spain and the months ahead of the European Championship in an open, constructive and intensive exchange," a DFB statement read.
"In the process, Joachim Low informed those involved about his assessments, ideas and further plans.
"The members of the Executive Committee agreed that what counts is the high-quality work of the coaching staff, the intact relationship between the team and the coach and a clear concept for the previous and future procedures.
"A single game cannot and must not be a yardstick for the general performance of the national team and the national coach."
Low has been coach of the German national team since 2006 and he led them to FIFA World Cup glory in 2014 in Brazil, beating Argentina 1-0 in the final.
