The first representative match was played at the KC Stadium on Monday evening, with a 24,000 crowd watching England beat Serbia & Montenegro 3-2 in an Under-21 fixture.
Among those praising the £42.5million council-owned stadium was the England U-21 coach David Platt.
He said: "I thought everything about our stay here in Hull has been tremendous. The stadium is top-class, the pitch was perfect to play on and the facilities offered to us were all that we needed.
"Hull City also did a very good job in ensuring that the ground was packed with 24,000 people even though this match was only a friendly international being played at the end of a long season. The fans who came were brilliant. Many places can boast full houses every week but it is what the supporters do when they are in there that counts and it was great to hear them all through the match. The noise was great and it really made for a good atmosphere.
"I will certainly be giving this my recommendation as the future venue for other international matches. It may not be big enough to host senior games but from our level down it is the ideal stadium and set-up. I hope we can come back soon."
Another FA official also confirmed it will be recommended that Hull hosts top fixtures in future. Next season's Conference Play-off Final is one event high on the Stadium Management Company's priority list for booking.