Berta, 53, assumes the role on a permanent basis with the Gunners as he replaces the outgoing Edu Gaspar, who resigned in November.
"I am thrilled to be joining Arsenal in what is a hugely exciting period for the club," Berta said in a statement.
"I have watched with great interest the way Arsenal has evolved in recent years and I have admired the hard work that has gone in to 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."
Berta emerged as the standout from a host of candidates to fill the position which included former Manchester United sporting director Dan Ashworth and ex-Arsenal midfielder Tomas Rosicky.
Berta spent 12 years at Atletico Madrid and helped launch the club back into contention for success in Spain alongside bohemoths Real Madrid and Barcelona.