حَتَّى أَدَّتْنِي خَاتِمَةُ الْأَطْوَافِ
Until the final round of my wanderings brought me along.
Ḥattā introduces the outcome of repeated movement. Khātimat al-aṭwāf refers to the last of his circuits or rounds.
The narrator has been moving by choice and necessity; now the final turn of the search seems itself to lead him somewhere.