The 21-year-old international, who was named the AFC Youth Player of the Year in 2013, made the move to the Serie A side from Turkey's Super League outfit Caykur Rizespor.
"I know all about Serie A. I chose Udinese because I feel they are a big club," Adnan told reporters at his unveiling at Udinese on Friday.
"I'm proud to be the first Iraqi footballer to play in Italy and I am prepared to play in any position. I want to be a success with Udinese.
"I believe I can handle myself against any forward in the world.
"I also want to thank all my Iraqi fans. They've given me immense support."
An attacking left-back often compared to Real Madrid star Gareth Bale, Adnan 25 caps for the national U-20 and U-23 teams and represented the senior national side 34 times.