Low had worn the tight sweater in group wins over Australia and Ghana in South Africa as well as their spectacular knockout round victories over England and Argentina.
His players had urged him at the time not to wash the sweater and keep wearing it during their fine run after he had briefly opted for a cardigan in their group stage defeat to Serbia.
Assistant coach Hansi Flick also sported a blue top in some of the matches.
The garment's luck seemed to run out when Germany were beaten in the semi-final by eventual winners Spain.
"This is a great idea," Low said in a statement. "This sweater is an unforgettable reminder of the World Cup in South Africa and the amazing time millions of fans, our players and coaches had."
The sweater will be on permanent loan from a private company and will be exhibited at the DFB football museum in Dortmund from 2014 onwards.
