Kiivit was born in Tuhalaane, Viljandi County on 27 February 1906 in the Governorate of Livonia.

In April 1933 he became a vicar in Jõhvi and in July 1933 he became a pastor in Emmaste, on the island of Hiiumaa.

On 2 February 1949, he was appointed Bishop of Tallinn and Primate of the Estonian Church.

On 31 August 1967 Kiivit resigned from the post of archbishop due to poor health, but also because of increasing distance from the state authorities.

[1] KGB archives opened after the collapse of the Soviet Union showed that Kiivit an NKVD/KGB agent who was first recruited in 1948.