The pair are Trinidad and Tobago internationals, and were celebrating after being drawn in the same group as England for June's competition.
The Valiants stars will also play Paraguay and Sweden in Group B of the Germany-based event.
Birchall scored the winning goal as Trinidad beat Bahrain in a two-legged play-off to reach the finals for the first time.
Vale chairman Bill Bratt said: "Chris is a brilliant lad and everyone at the club is extremely proud of him. It's a massive achievement and he's the first home-grown Vale player to play in a World Cup finals.
"Chris' achievements with Trinidad & Tobago have raised the profile of the club and undoubtedly made him a better and more confident player - long may it continue."
England will play Trinidad and Tobago in Nuremberg on June 15.