England lifted the trophy on the basis of the boundary count as runs were tied in both the 50-over match and the Super Over.
Williamson was presented with the award during the drawn second Test between his team and England on Tuesday.
Kumar Sangakkara, the president of the Marylebone Cricket Club, one of the creators of the award, said New Zealand are worthy winners of the award.
"The New Zealand team are worthy winners of this award. In the heat of battle, they displayed a level of sportsmanship that was fitting for such a fantastic final, and indeed tournament," International Cricket Council (ICC) quoted Sangakkara as saying.
"It is a testament to their squad that even after a match that will live long in the memory for the cricket that was played, we are still talking about the Spirit of Cricket. Their actions deserve this recognition," he added.
The award, which was created in 2013, was the brainchild of the MCC and the British Broadcasting Corporation (BBC). It was created in memory of Martin-Jenkins, the former MCC president and BBC Test Match Special commentator, to honour his longstanding passion and desire to see the game played in the right spirit.