The 19-year-old is yet to feature for the second-tier club's first XI but will move to the Bundesliga club at the end of the season.
Ott had been the subject of speculation linking him with a switch to the Grundig Stadion and his arrival was welcomed by Martin Bader, Nuremberg's head of sports and public relations.
"Mike is one of the most talented players in Germany and has shown outstanding performance in his first senior year in the Under-19 and Under-23 sides at 1860 Munich," he told the club's official website.
"It is well-known that reputable clubs have made every effort (to sign) Mike. Therefore we are pleased that he has chosen FC Nuremberg."
Ott has scored 12 goals in 24 appearances for 1860's under-23 team in the Regionalliga this term.
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