He was 79 and had been suffering from pneumonia.
He had led the Assyrian Church of the East since 1976 and had met Pope John Paul II, Pope Benedict XVI and Pope Francis.
In a statement the Church said: "His Holiness had dedicated his entire life, to serving our Lord and our Holy Church.
"All his life he worked hard to be a spiritual father to us all. Heaven has welcomed him today and may he rest in peace."
The funeral service will be held on April 8 at St George Church in Chicago.