The versatile attacker will formally sign for HSV when his contract with FC Ingolstadt expires at the end of the month.
BILD says HSV boss Dieter Hecking was key to the deal, with Norwich having offered Kittel a contract worth €2m-a-year - almost treble his Ingolstadt wages.
The Canaries were convinced of an agreement before Hecking's intervention.
The coach invited Kittel to his family home where he set out his plans for the attacker - which was enough to convince him to turn down Norwich.
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