Dyke saluted the much-travelled Hodgson's 40-year managerial career, comparing him to leading English coaches of the past like Bobby Robson, Don Howe and Dave Sexton.
"I am constantly amazed by supporters' reaction to Roy if you go to a game with him. He is genuinely liked," Dyke told www.thefa.com.
"It is fascinating. Wherever we travel, people from different countries seek out Roy to share an experience they had of watching one of his sides, or talking to him about a player he once would have managed, or a coach that he knew.
"He's probably done more for the FA's international relations than anyone," added Dyke.
Hodgson is in his fourth year as England manager, having previously had stints in Italy, Switzerland, Finland, Denmark, Norway and United Arab Emirates.
The 68-year-old is now plotting his campaign for the European Championship finals in France in June, having overseen a 100 percent winning record in 10 qualifying matches.
"Roy is a great example to any aspiring coach that being open to new experiences and cultures can really develop you as a person," said Dyke.
"His CV is quite remarkable and it is hard to think of another coach of his stature that has been prepared to learn and grow the way he has.
"What a fantastic achievement, 40 years coaching at the level he has puts him up there with the great English coaches, much-revered people like Bobby Robson, Dave Sexton and Don Howe," added Dyke.
"We're very proud that, as England manager, Roy celebrates 40 years of coaching at the highest levels of our game. Long may it continue."
England have been drawn in European Championship Group B along with Wales, Russia and Slovakia.
(Writing by Tony Jimenez; Editing by Mark Lamport-Stokes)
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