How can Jesus be fully human and fully God?

How could Jesus be fully God and fully human at the same time? Is there any Scriptural support for this concept of hypostatic union? 

In all of history, there is only one Person (Jesus of Nazareth) who could claim full deity and full humanity at the same time. So, we have no scope to explain the union of divine and human nature using an earthly example, because there simply isn’t anyone like Jesus. In dealing with the hypostatic union, we must keep a few things in mind:

• Jesus is the eternally begotten Son of the eternal Father. He was with the Father from the beginning, equal to the Father in essence, possessing all of the divine attributes. Therefore, He has a divine nature for all of eternity (John 1:1, 2; Philippians 2:6, Hebrews 1:3).
• He has a fully human nature that is just like ours, with the exception of sin. He was born; He grew, learned, hungered, thirsted, slept, wept, showed emotions, and experienced joy, sorrow and every other human experience (Luke 2:7, 52; 4:2; 8:23; 10:21; John 11:35, Mark 14:33). 
• Unlike His divine nature, the human nature of Jesus had a beginning at the incarnation. At incarnation, the divine Son of God took on an additional nature, namely, the human nature, to go along with His divine nature (John 1:14, Philippians 2:7, 8).
• From the time of incarnation, He would be the perfect God-man in all of history, and forever in eternity future. There is no end to His humanity once death and resurrection took place either. He will always have these two natures existing together. He calls himself the Root and the descendant of David in His post-ascension appearance to apostle John in Patmos (Revelation 22:16), referring to His divine nature (of claiming to be David’s God) and His human nature (by claiming His descent by birth from the genealogy of David).

There was no end to Jesus’ humanity once death and resurrection took place. He will always have these two natures existing together

Thus, we can understand, without confusion, from these Scripture portions that Jesus has two natures. They are inseparable, unchangeable and indivisible. In other words, there is no division of persons called divine Jesus and human Jesus. There is one Person, Jesus Christ, who is both God and man at the same time. 

Dual nature

We must also remember two more truths to make sense of the hypostatic union (i.e. the combination of divine and human natures in the single person of Christ). 

1. Some actions done in one nature cannot be true of the other nature. Jesus being hungry belongs to His human nature. It cannot be true of His divine nature, as hunger is not something that divine beings have. Conversely, Jesus claiming His omnipresence where two or three are gathered in His name is something that belongs to the divine nature. This cannot be said of the human nature bound by time and space.
2. Any actions done within either of these two natures are attributed to the whole Person of Jesus. When Jesus thirsted for water, we cannot say that the human Jesus thirsted; when Jesus calmed the storm, we cannot say that the divine Jesus calmed the storm. It is scripturally right to say that Jesus hungered or Jesus calmed the storm.

When Jesus thirsted for water, we cannot say that the human Jesus thirsted; or that when He calmed the storm, it was the divine Jesus who calmed the storm

Take it from Scripture

The gospels contain many evidences of Jesus displaying His full deity and humanity at the same time. Here are a few of them:

1. Jesus was hungry (Luke 4:2, Mark 11:12), but He also fed thousands of people at the same time (Matthew 14:13-21; 15:32-39).
2. He was thirsty for water (John 19:28) and, at the same time, He offers springs of water welling up to eternal life (John 4:14). 
3. Jesus increased in wisdom (Luke 2:52), yet spoke of not knowing the day nor the hour of His coming (Mathew 24:36). Yet, at the same time, He claimed intimate and comprehensive knowledge of the Father and of being known by the Father (Mathew 11:27). He is also aware of the inward thoughts and intentions of man (John 1:47-51; 2:24, 25, Mark 2:8).
4. Jesus proved from Psalm 110 in Mark 12:35-37 that He is both the Lord and descendant of David.
5. Jesus expressed astonishment as though He saw something He never expected (Mathew 8:10); yet, there are other occurrences where He knows what the possible outcome of an action could have been (Matthew 11:20-24).
6. There are instances where Jesus prays (Mark 1:35, Luke 6:12, 9:18, 28; 11:1, Mathew 26:36, John 17) and there are instances where He claimed to answer prayers (John 14:13,14).
7. Jesus goes from the world to the Father physically through Ascension (John 16:28, Luke 24: 51). Yet, He promises His presence with us to the end of the age (Matthew 28:20).

There are more such points of observation, but these examples prove for sure that there is no one in the world who is both divine and human at the same time. This fully divine and human person was necessary to be the perfect mediator between God and man to facilitate our redemption so that we become sons of God.