Fr. Paul N. Harrilchak notes in his book, The Divine Liturgy of the Great Church (p 211), that the origins of the Apostle’s Fast are rooted in the ancient Christian practice that there was no fasting or penitential kneeling in the Church for the 50 days from Pascha to Pentecost, which for many centuries was treated as one continuous and great Feast in the Church which lasted 7 weeks plus one day. In the 4th Century according to documents, following this totally fast-free fifty day festal period, plus an additional week of feasting after Pentecost, a one week fast was observed. That one week fast which began 8 days after Pentecost morphed, under monastic influence in recent centuries, into the Apostle’s Fast which now stretches from the Monday after All Saints Day until the Feast of Ss Peter and Paul on June 29. Because Pascha and Pentecost are movable feasts, the length of the Apostle’s fast changes each year.
After having celebrated Pentecost, keep a feast for one week, and after that keep a fast for one week [origin of the so-called Apostles’ Fast–Ed.]: for it is right to rejoice over the Gift of God [meaning the Descent of the Holy Spirit–Ed.], and then to keep a fast after the time of relaxation [of Wednesday/Friday fasting during the 50-day Paschal/Pentecost season]. (Apostolic Constitutions, Syria (ca. 380 A.D.).