As Old As The Belief In The Hypostatic Union

The special and formal devotion to the Heart of Jesus, which is now so popular in the Church, owes its origin to a French Visitation nun, St. Margaret Mary Alacoque, who lived in the latter part of the seventeenth century. Her biographers relate that our Lord Himself appeared to her and declared that this worship was most acceptable to Him; and her director, the famous Jesuit, Father Claude de la Colombiere, preached the devotion at the Court of St. James's, and zealously propagated it elsewhere. The most popular book in defence of the new devotion was that of Father Joseph de Gallifet, S. J., "De Cultu SS. Cordis Jesu in variis Christiani orbis partibus jam propagato." It was published with a dedication to Benedict XIII. and with the approval of Lambertini (afterwards Benedict XIV.); the French translation appeared in 1745, at Lyons. On February 6, 1765,1 Clement XIII. permitted several churches to celebrate the feast of the Sacred Heart, which was extended in 1866 to the whole Church. It is generally kept on the Friday (in the U. S. as other countries) after the Octave of Corpus Christi. In England, Italy, France, Netherlands, Germany, Spam and Portugal, indeed throughout the Catholic world, the devotion and the feast found a ready and enthusiastic acceptance. However, the worship of the Sacred Heart encountered keen opposition, particularly from the Jansemsts. They who practised it were nicknamed "Cardiol a tree" or "Cordicolse," and charged with Nestorianism, as if they worshipped a divided Christ, and gave to the created humanity of Christ worship which belonged to God alone. The Jansenist objections were censured as injurious to the Apostolic See—which had approved the devotion, and bestowed numerous indulgences in its favour—by Pius VI. in his condemnation of the Jansenist synod of Pistoia. This condemnation was issued in the bull "Auctorem fidei," bearing date August 28, 1794. A further approval of the devotion was The Congregation of Rites had refused to sanction the feast in 1697 and 1729.implied in the beatification of Margaret Mary Alacoque in 1864. The bull "Auctorem fidei" contains the following explanation of the principle on which the devotion rests, an explanation which is at once authoritative and clear. The faithful worship with supreme adoration the physical Heart of Christ, considered "not as mere flesh, but as united to the Divinity." They adore it as "the Heart of the Person of the Word to which it is inseparably united." It is of course absurd to speak of this principle as novel; it is as old as the belief in the hypostatic union, and it was solemnly defined in 431 at the Council of Ephesus. 

All the members of Christ united to the rest of His sacred humanity and to the eternal Word are the object of divine worship. If it be asked further, why the heart is selected as the object of special adoration, the answer is, that the real and physical heart is a natural symbol of Christ's exceeding charity, and of his interior life. 

Just as the Church in the middle age3 turned with singular devotion to the Five Wounds as the symbol of Christ's Passion, so in these later days she bids us have recourse to his Sacred Heart, mindful of the love wherewith he loved us "even to the end." Nothing could be made of the fact, if it were a fact, that the devotion actually began with Blessed Margaret Mary, for though the doctrine of the Church cannot change, she may, and does from time to time, introduce new forms of devotion. But the special devotion to the Heart of our Saviour is as old at least as the twelfth century, while early in the sixteenth the Carthusian Lansperg recommended pious Christians to assist their devotion by using a figure of the Sacred Heart.

Link (here) the Catholic Dictionary

Go (here) to the Protestant Dictionary view of the Sacred Heart of Jesus