Loew's contract runs until 2022, having been extended for two years in May. But his side's shock exit in Russia after defeats to Mexico and South Korea and a solitary win over Sweden had sparked speculation about whether he would keep his job.
"We are all firmly convinced that with Jogi Loew, we have a national coach who will analyse (the situation) very precisely, take the right steps and lead our team back on the road to success," DFB president Reinhard Grindel said in a statement.
Grindel said Loew would present his analysis of what went wrong before the team's next international on Sept. 6 against France for the newly created Nations League.
The 58-year-old has been in charge for 12 years, having taken over after the 2006 World Cup. In 2014 he led Germany to their fourth World Cup title.
He had previously been an assistant to his predecessor Juergen Klinsmann from 2004-2006.
Loew, who prior to Russia had led his country to at least the semi-finals in all major tournaments, said he was "very grateful for the confidence that the DFB continues to place in me."
"My disappointment is equally big, but I want to start the reconstruction with all my strength. I will now analyse everything with the team, we will have talks and (I) will draw my conclusions prior to the season start in September."
Germany's first-round World Cup exit was its earliest in 80 years. The international careers of several of its 2014 champions, including Mesut Ozil, Sami Khedira and Jerome Boateng, remains in doubt.
Loew has been in charge for 165 matches, winning 108, more than any other Germany coach.
Until a few years ago his team were an indomitable attacking force, and their 7-1 demolition of Brazil in the 2014 World Cup semi-final was considered a remarkable achievement.
But they managed just two goals in their three group matches in Russia to exit the tournament in shame, leaving German fans, used to much greater success, bitterly disappointed.
(Writing by Brian Homewood, editing by Ed Osmond and Hugh Lawson)
