Construction started in 1295 by the Aragonese settlers, but was only finished in 1342 with financial support from Diego of Barzona, who was Count of Barzona and the most powerful military commander and landowner in Brunant at the time. The church of the abbey was completed in 1314.
The abbey near Alzar was the first Cistercian monastery on the Brunanter islands; the first monks arrived from France in the late 1290s and worked on finishing the complex for decades. The Alzar Abbey became the mother abbey for all future Cistercian monasteries in Brunant.
By the early 16th century, the abbey fell into disrepair. The Counts of Barzona, who were the abbey's main financial supporters, lost their wealth in the late 15th century, and the foundation of the Kingdom of Brunant saw little support for the Alzar Abbey. Around the 1520s, the last Alzar monks left for a newly-built monastery in Roodstad, where the Cistercians had built the St. Robert's Church from the 1460s on.
Since the late 19th century, the former Alzar Abbey has been subject to several archaeological excavations, but most of the liturgical objects, documents and manuscripts and art were taken by the monks, stolen or destroyed through the ages. Only a handful of stones is left.