The Italian arrives after over 12 years involved with Atletico Madrid.
Berta succeeds Edu Gaspar, with the Brazilian leaving the role earlier this season.
He said: “I am thrilled to be joining Arsenal in what is a hugely exciting period for the club.
“I have watched with great interest the way Arsenal has evolved in recent years and I have admired the hard work that has gone into re-establishing the club as a major force in European football with a passionate following around the world.
“The club has great values and a rich history, and I am looking forward to playing my part in shaping a successful future with a great team. I cannot wait to get started in my new role and I am really looking forward to experiencing my first game at Emirates Stadium together with our supporters.”
Co-Chair Josh Kroenke added: “Anyone who knows football knows Andrea is an impressive figure. He has vast knowledge of the game, a great track record, a strong network and an insatiable desire to build winning teams.
“Andrea will be a great addition to our club. He understands our values and what we stand for and we have no doubt he will help us push on and take the next steps in our bid to win major trophies.
“We undertook a thorough recruitment process and we were hugely impressed with the level of all the other candidates, but it was Andrea’s experience and the success he has enjoyed that stood out. “We are really looking forward to working together and welcoming him into the Arsenal family.”