The election of the new abbot was confirmed by Pope Leo XIV on Friday.
The abbey of the Augustinian canons is considered to be the oldest monastery in the West that has existed without interruption. It reports directly to the Pope.
Ineichen's predecessor Jean César Scarcella resigned at the end of June.
The move followed years of massive accusations regarding the handling of sexual abuse by the monastic community.
In its report published in June, an independent commission of enquiry commissioned by the Order of Augustinian Canons had found that there had been at least 67 cases of sexualised violence between 1960 and 2024, mostly against minors, perpetrated by at least 30 monks.
The abbey then asked for "unconditional forgiveness" and announced an action plan.
Among other things, an independent contact person is to be appointed for those affected.