Abbot Kevin, who leads the Benedictine community of monks in West Sussex, was elected in June 2010 and turned 80 the following year.
"When I was elected Abbot in 2010, I realized that, because of my age, it was improbable that I would complete the eight-year office," the abbot said in a general communication.
He explained that following discussions with the Abbot President of the English Benedictine Congregation (EBC), Fr Richard Yeo, he has decided to step down on 2 June, exactly three years since his election.
"Both he and I are of the opinion that now would be an appropriate time for me to step down, and allow the community to consider a young person for the role of abbot," he added.
Abbots in EBC communities are elected for eight-year renewable terms.
The election of a new abbot will take place in early August and from 2 June Fr Luke Jolly, the prior, will act as superior of the abbey.
Worth was founded as a daughter house of Downside Abbey, in Somerset, in 1933.
The community has 25 monks and run a school, parish and retreat house.
In 2005 it gained wider prominence when it featured in a BBC Two programme The Big Silence.