This sounds like the Inheritance Cycle -- Eragon, Eldest, Brisingr, and Inheritance -- by Christopher Paolini. https://en.wikipedia.org/wiki/Inheritance_Cycle has a decent synopsis.
As far as I remember, there are no tattoos mentioned. However, every other thing you mention is represented. Eragon is a young (he is fifteen years old when the series starts) male who impressed a Dragon, is taught the magic of the Elves, falls in love with an Elf, Arya, whose mother is Queen of the Elves. Eragon is transformed into an Elf during the Elves' Blood-Oath Celebration, which happens once every one hundred years, by the spirit of the dragons who gave Elves (and later, humans) the ability to perform magic.
The Elves are at war with Galbatorix, a Dragon Rider who violated his oaths to seek personal power. He is currently the king of Alagaësia. Galbatorix and his thirteen Forsworn have killed all the other Dragon Riders (except Eragon). Except for Galbatorix, all of the Forsworn are dead. The only magic users, and thus the only threat to his magical tyranny, as far as Galbatorix knows, are the Elves.
Tattoos as a representation of magic power remind me of two other series.
The first series is Wen Spencer's Tinker/Elfhome series -- the Sekasha caste of elves have protective magics tattooed on their bodies in the color of the clan of the person they defend. (Wind is Blue, Fire is Red, and Stone is Black. I think Water is White, though members of that clan have been conspicuous by their absence so far.) Even though Tinker is female, she does not act like a "typical" female; she's an eighteen-year-old absent-minded inventor who loves magic (great-great-great-granddad was an Elf stranded on a magic-poor Earth. Tinker and her male cousin -- who acts more like a brother -- Oilcan has inherited the genetic code to use the Elven Spellstones), hovercraft racing (she invented the hovercraft) and quantum physics.
The other series, the House of Night series by P. C. Cast + Kirstin Cast currently stands at twelve books, four novellas, and four "related books". Its only similarity to the books you're describing is the swirly tattoos that grow as the magic power of the individual grows. They appear on the face during puberty (when a strand of "junk DNA" gets activated and turns the unfortunate teen into a vampire. The tattoos do grow as the individual's power grows. I don't remember any elves. A war between factions of the House of Nyx (where the newly converted vampires attend school for four years and learn to use their powers (as well as mundane subjects like geography and mathematics), boils over into open warfare in later books.