When the life-giving Word of God dwelt in human flesh, he changed it into that good thing which is distinctively his, namely, life; and by being wholly united to the flesh in a way beyond our comprehension, he gave it the life-giving power which he has by his very nature. Therefore, the body of Christ gives life to those who receive it. Its presence in mortal men expels death and drives away corruption because it contains within itself in his entirety the Word who totally abolishes corruption.

From a commentary on the Gospel of John by Saint Cyril of Alexandria

Jesus, being God, has life-giving power within Himself. Therefore, when we receive His Body and Blood He bestows that life to us who worthily receive Him. That is why He said, “he who eats my flesh and drinks my blood has eternal life, and I will raise him up at the last day.” (John 6:54)