Well, personally I'm also a fan of stories like Regios, and I can tell you finding similar ones is quite difficult, the most similar ones would probably be:
Anime: (the first five are based in light novels)
Densetsu no Yuusha no Densetsu which not exactly portraits the type of "school transfer" that you want, but I found both of the main characters quite similar to Regios' characters.
Hagure Yuusha no Estetica is probably a bit more similar with the main character returning to "Earth" after succesfully defeating the demon lord in another world and enrolling a special school for returnee heroes where he ends up being one of the strongest ones. The only thing is that it has a lot of fan-service(in case you don't like that).
Mondaiji-tachi ga Isekai kara Kurusou desu yo hasn't even aired but from what I've read it seems a little bit like what you're looking for, two girls and one boy with special gifts are transfered to another world in order to save a community there from the demon lord. At least in the manga version the main guy was really powerful from the beginning.
Infinite Stratos in a way, the main character is forced to enroll the school just for being the only man able to pilot the mechas.
Ichiban Ushiro no Daimou, in here he doesn't transfer but just enroll in the academy and ends up learning he's the almighty demon lord which makes him get alienated (then again it also has a lot of fan-service).
Dog Days again more of a "transfer to another world" one, the main guy (Cinque or Sink however you want to call him) was the 2nd place in an athletics championship which ends up making him a hero on the other world. It's an original anime.
Muv-Luv Alternative: Total Eclipse is based on a visual novel, while it doesn't have a school setting, the main guy gets transfered to a testing facility in Alaska from an elite testing facility elsewhere in America even though he's extremely skilled because of an incident.
Natsume Yuujinchou isn't probably exactly what you're looking for but you might as well check it out, the guy changes schools since he is being like passed around between his relatives after being left orphan and being the only one in his surroundings able to see youkai. It's based on a manga which I haven't read but I guess it should be as good.
Persona 4 is based on a game, here the guy is transfered for family issues and while he isn't almighty from the beginning it's the kind of MC that's always above the rest of the characters.
Manga:
Ao no Exorcist, in a way, even if they never show you the first school he attends he ends up being transfered. (The anime isn't as good as the manga after it enters the filler in ep 15 so you might as well only read the manga)
Shokugeki-no SOMA is a brand new series, even if it's about cooking the rest of the setting is exactly what you wanted (then again this is also a bit heavy on fan-service)
Asu no Yoichi also has an anime which isn't all that bad, but the manga is better. It has a samurai going down the mountain he lived in and transfering to a school in the city where he's the best fighter. Again, it has its good share of fan-service.
The list ended up being bigger than I expected, I didn't actually think I could find this much when I began writing this, even if not all meet all your requests I hope there's one you haven't seen/read that you like.
