There is no place in Loew's squad for Goetze, who scored the winning goal in the 2014 World Cup finals, after an erratic season at Borussia Dortmund.
Remembering that he first walked through the doors of Italy's Coverciano training camp in 1978 with the under-14 team, Mancini said it was the right moment in his career to take on the challenge of coaching his country.
Low said: "Working together with Andy Kopke, Thomas Schneider, Marcus Sorg, Oliver Bierhoff and our entire team behind the scenes, we are working to develop the best players in Germany and make them better, to form a team going for the highest goals in football".
Gotze scored in extra time, beating Argentina with a goal in the 113th minute in the World Cup final on July 13, 2014 at the Maracana in Rio de Janeiro, Brazil.
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"Marco is a special weapon, he has special gifts", Loew said.
Loew opted for Petersen over Bayern Munich forward Sandro Wagner, giving the Freiburg player his first call-up to the national team after an excellent season. "He has great intelligence in the game and in the second half of the season he was in really good form".
Loew has also selected Mesut Ozil and Ilkay Gundogan despite the pair landing in hot water with the German FA over the weekend after the Premier League stars posed for pictures with Turkey President Recep Tayyip Erdogan.
Germany will begin its World Cup defense with group games against Mexico, Sweden and South Korea.