The Saturday observance is a commemoration of God's creative act (Gen. 2:2-3).
Genesis 2:2-3 Since on the seventh day God was finished with the work he had been doing, he rested on the seventh day from all the work he had undertaken.  So God blessed the seventh day and made it holy, because on it he rested from all the work he had done in creation.
During the era of the Old Covenant it was fitting that the People of God commemorate the 7th Day, Saturday, as the day of rest dedicated to the Lord.
Christians are the People of God of the New Covenant. The first day of the week, the day of the Resurrection, the day on which Pentecost occurred, is the day we commemorate. It stands for "re-creation," the Redemption, being the eight day, first day of the week following the Sabbath of creation rest. "Behold I makes all things new" (Rev. 21:5). The English name Sunday does not express this well. However, Latin (the language of the Church) call this day Dominica or The Lord's, a fitting name for the Christian Sabbath.
From the very beginning the Apostles, exercising the authority given them by Christ, made determinations of the applicability of the Mosaic Law to the Church (Acts 15).
Acts 15:28 'It is the decision of the holy Spirit and of us not to place on you any burden beyond these necessities. . .
The celebration of Sunday was one of those decisions, in constant use since. This was so universally known in the early Church it is not even mentioned in Scripture, though implicit in Acts 20:7 and 1 Cor 16:2.
Acts 20:7 On the first day of the week when we gathered to break bread, Paul spoke to them because he was going to leave on the next day, and he kept on speaking until midnight.
1 Cor. 16:2 On the first day of the week each of you should set aside and save whatever one can afford, so that collections will not be going on when I come.