“I am the living bread which came down from heaven; if any one eats of this bread, he will live for ever; and the bread which I shall give for the life of the world is my flesh. … For my flesh is food indeed, and my blood is drink indeed.”
Short answer
Jesus said "my flesh is food indeed" and let disciples leave over that saying. At the Last Supper he said "this is my body." Paul warns that receiving unworthily profanes the body and blood of the Lord. From Ignatius of Antioch at the start of the second century to Augustine in the fifth, the Fathers quoted here call the Eucharist the flesh and blood of Christ. The Council of Trent rejected by name the view that Christ is present only as in a sign or figure.
Built from two project documents: Scriptural Evidence for the Real Presence, and Eucharistic Quotes by Church Fathers. Every quotation was then checked against the linked source, and the wording now follows the translation on the linked page. Five quotations in the Fathers document could not be found on an approved source or did not hold up when read in context: Clement of Alexandria, Hippolytus, Ephrem, Athanasius, and Augustine's Sermon 227. Four were replaced with verified witnesses and Ephrem was removed. The Council of Trent and the Catechism were added to bring the timeline to the present.
Where this teaching appears on the Offshoots timelines: before 1384, The Eucharist as a figure: John Wycliffe; January 1528, The Lord's Supper without a bodily presence; October 1529, The Reformers divided on the Lord's Supper; 1530, The Lutheran confession rejects the denial of the presence; 1551, The Church's reply on the words "This is my body".
18 quotations in date order
“Many of his disciples, when they heard it, said, "This is a hard saying; who can listen to it?" … After this many of his disciples drew back and no longer went about with him. Jesus said to the twelve, "Will you also go away?"”
“Take, eat; this is my body. … Drink of it, all of you; for this is my blood of the covenant, which is poured out for many for the forgiveness of sins.”
“The cup of blessing which we bless, is it not a participation in the blood of Christ? The bread which we break, is it not a participation in the body of Christ?”
“Whoever, therefore, eats the bread or drinks the cup of the Lord in an unworthy manner will be guilty of profaning the body and blood of the Lord. … For any one who eats and drinks without discerning the body eats and drinks judgment upon himself.”
“They abstain from the Eucharist and from prayer, because they confess not the Eucharist to be the flesh of our Saviour Jesus Christ, which suffered for our sins, and which the Father, of His goodness, raised up again.”
“Take heed, then, to have but one Eucharist. For there is one flesh of our Lord Jesus Christ, and one cup to [show forth ] the unity of His blood; one altar; as there is one bishop, along with the presbytery and deacons, my fellow-servants”
“For not as common bread and common drink do we receive these; but in like manner as Jesus Christ our Saviour, having been made flesh by the Word of God, had both flesh and blood for our salvation, so likewise have we been taught that the food which is blessed by the prayer of His word, and from which our blood and flesh by transmutation are nourished, is the flesh and blood of that Jesus who was made flesh.”
“For as the bread, which is produced from the earth, when it receives the invocation of God, is no longer common bread, but the Eucharist, consisting of two realities, earthly and heavenly; so also our bodies, when they receive the Eucharist, are no longer corruptible, having the hope of the resurrection to eternity.”
“…the flesh feeds on the body and blood of Christ, that the soul likewise may fatten on its God.”
“But we give thanks to the Creator of all, and, along with thanksgiving and prayer for the blessings we have received, we also eat the bread presented to us; and this bread becomes by prayer a sacred body, which sanctifies those who sincerely partake of it.”
“So then after having carefully hallowed your eyes by the touch of the Holy Body, partake of it; giving heed lest you lose any portion thereof … Will you not then much more carefully keep watch, that not a crumb fall from you of what is more precious than gold and precious stones?”
“As to the verity of the flesh and blood there is no room left for doubt. For now both from the declaration of the Lord Himself and our own faith, it is verily flesh and verily blood. And these when eaten and drunk, bring it to pass that both we are in Christ and Christ in us.”
“Rightly, then, do we believe that now also the bread which is consecrated by the Word of God is changed into the Body of God the Word.”
“The cup of blessing which we bless, is it not a communion of the Blood of Christ? Very persuasively spoke he, and awfully. For what he says is this: This which is in the cup is that which flowed from His side, and of that do we partake.”
“For He took upon Him earth from earth; because flesh is from earth, and He received flesh from the flesh of Mary. And because He walked here in very flesh, and gave that very flesh to us to eat for our salvation; and no one eats that flesh, unless he has first worshipped: we have found out in what sense such a footstool of our Lord's may be worshipped, and not only that we sin not in worshipping it, but that we sin in not worshipping.”
“If any one denieth, that, in the sacrament of the most holy Eucharist, are contained truly, really, and substantially, the body and blood together with the soul and divinity of our Lord Jesus Christ, and consequently the whole Christ; but saith that He is only therein as in a sign, or in figure, or virtue; let him be anathema.”
“In the most blessed sacrament of the Eucharist "the body and blood, together with the soul and divinity, of our Lord Jesus Christ and, therefore, the whole Christ is truly, really, and substantially contained." "This presence is called 'real' - by which is not intended to exclude the other types of presence as if they could not be 'real' too, but because it is presence in the fullest sense: that is to say, it is a substantial presence by which Christ, God and man, makes himself wholly and entirely present."”