Honestly, I hate typology. At least, typology that isn’t given interpretation to us by the writers of Scripture. Obviously, those ways in which God has given us preview of the wonder He will do in Christ are to be cherished. When I say “typology” I mean the typology so common in evangelical pulpits. I know that as a younger person I “Ooohed” and “Aaahed” at each brilliant “insight” offered into the symbolism of the Bible by those in the pulpit. Now I’ve come to see that as an expression of those who won’t,don’t, or can’t be satisfied by the clear meaning of the text. Because of that background I am loathe to wade out into typological waters. However, thanks to Monergism, I was able to find helpful resources (listed below) that enabled me to meet the requirements of my class on John without it turning into an exploration of the depths of eisegesis. Below is the “fruit” of my attempt to answer the question in the subject line.
In seeking to discuss how Christ fulfills the symbolism of the Feast of Booths we must begin with a note about the peril of attempting to speak of the consummation of typology where the Apostolic writers have offered no explanation.
Obviously, all of scripture is about Jesus Christ. We know well from other NT passages that the customs of the Jewish people often provide symbolic or typological references to the coming redeemer. However, this principle – as a multitude of commentators have well proven – often drives those who would seek “deeper” meaning in the Biblical text to extremes warranted neither by the text itself nor rationality. Therefore when discussing typology the careful student chooses to “tread carefully” in order not to do injustice to God’s Word.
With that in mind we consider the Feast of Booths and it’s consummation in our redeeming Lord, Jesus Christ. As is well know, the celebration of the Feast of Booths was commanded by God in Leviticus 23:41-43 as a means by which the nation would remember how God mightily brought them out of the land of Egypt.
Here we see our first opportunity to safely interpret how it might be said that Christ fulfills the symbolism of the Feast of Booths, namely that a feast dedicated to remembering God’s deliverance of His people from slavery (physical) would find it’s ultimate fulfillment in the One who would ultimately deliver God’s people from slavery (spiritually) to sin. This can point to none other that the Lord Jesus Christ, the great liberator.
Further, the Feast of Booths was a feast which prominently featured a sacrifice, leading Tony Warren to rightly conclude that this particular feast “was to be accompanied by a sacrifice, which was an indication that they would ultimately find their fulfillment in Christ’s death!”  We know that each and every OT sacrifice was a poor and weak sacrifice, able ultimately to provide nothing like a permanent restoration of man to the God he has offended. However, we also know (from the same text – Hebrews 10:1-10) that God’s offering of His Son to Himself is able to perfectly make atonement for mankind and allow God to bring His people to Himself. Thus we find a second fulfillment of symbolism in the Feast of Tabernacles in the person of Jesus Christ.
The final fulfillment, at least for our purposes, is found in the ceremony of the festival. David Rice quotes the commentary by Jameson, Fausset, and Brown to explain the custom: “The generally joyous character of this feast broke out on this day into loud jubilation, particularly at the solemn moment when the priest, as was done on every day of this festival, brought forth, in golden vessels, water from the stream of Siloah, which flowed under the temple-mountain, and solemnly poured it upon the altar. Then the words of Isaiah 12:3 were sung, `With joy shall ye draw water out of the wells of Salvation.â€™” Rice sees a likely connection between the particulars of this ceremony and the words of Christ recorded in John 7: “What an appropriate moment for our Lord to step forth and declare that in him was the fulfillment of the prophecy: ‘He that believeth on me, as the scripture hath said, out of his belly shall flow rivers of living water’ (John 7:38). This was an offer of everlasting life to those who would drink freely of this living water.” 
Thus do we easily find three ways in which Jesus Christ fulfills the symbolism of the Feast of Booths without having to stray into the grosser forms of typological interpretation. Ultimately, these three points should lead us to rejoice in our salvation in the person of Jesus Christ. That which was only pointed to in days gone by we have the blessing of living in the fulfillment of – all because of the work of our Savior.