The Romania Under-16 captain, who had also been linked with Inter, has agreed a three-year deal with the Gunners and will be a first-year scholar at the club next season
The 16-year-old is the Gunners' first signing of the summer transfer window and will join the club's academy as a first-year scholar.
Dragomir, who captains the Romania Under-16s, had been linked with Inter but admitted that the chance to join Arsenal was too tempting to turn down.
“The Arsenal offer seemed the best to me, I felt that this is my place,” Dragomir told Pro Sport following the move.
“I am very glad [to sign] and I hope not to disappoint anyone.”
Dragomir's agent, Catalin Sarmasan, added: “I offered Vlad to Arsenal a year and a half ago and they have monitored him closely.
“In my opinion, he is one of the most talented young players in Europe at the moment.”