Agnelli will replace Bayern Munich president Karl-Heinz Rummenigge, who has held the position since 2008 but has decided to step down.
"My predecessor, Karl-Heinz Rummenigge, has set a great example and has set the bar of achievements at a very high level," Agnelli said following his appointment.
"I am looking forward, together with the Executive Board and the Administration, to build on his significant results as we manage ECA in the coming years.
"It is a huge honour and a great responsibility the European clubs have entrusted me with.
"I am looking forward to working closely with all stakeholders within the game in order to protect, promote and develop club football at all levels across Europe."
The ECA, whose 220 members include the most powerful and wealthy of the continent's football clubs, has named Agnelli and Arsenal chief executive Ivan Gazidis as their representatives on UEFA's Executive Committee.
Rummenigge was awarded an honorary chairmanship in recognition of his work.