It was founded in the early 12th century, shortly after the foundation of Garsten Abbey, by the local nobleman, Arnhalm I of Glunich, who gave his castle for conversion to a monastery. The premises, dedicated to Saint Andrew, were ready for occupation in the 1120s. Gleink was settled from Garsten Abbey, from where the first abbot, Ulrich, came. The family of the original founder, after running short of money, were obliged to pass the position of "Vogt" (lord protector) to Leopold the Strong, Margrave of Styria, who also issued the foundation charter in 1125 and endowed the abbey with property, notably around the present Gleinkersee.