The Minstermen lifted the FA Trophy at the famous stadium on May 12 thanks to a 2-0 win over Newport and duly followed that up eight days later with a 2-1 victory over Luton in the play-off final to clinch promotion.
Two commemorative granite stones marking both victories are to be included in a Wembley Way project and will soon be situated alongside similar tributes to famous victories and players who have played a part in the stadium's history, including England's 1966 World Cup winning side.
City manager Gary Mills and his squad returned for pre-season training on Friday and were presented with two replica stones and a letter of congratulations from FA chairman David Bernstein.
Mills said: "The stones are absolutely beautiful and will always be there for everybody to see now.
"Nobody will be able to take those achievements away from us and, when we move to a new stadium, the replicas will be put in the right place. To get that recognition at Wembley as well is fantastic."