The scriptures to be considered for this question come from Matthew 26:26-30, Mark 14:22-26, Hebrews 4:14-16, Hebrews 5:1-11Hebrews 6:20, Hebrews 7, Psalm 110:1-7, especially verse 4, about our Lord and is introduced in Genesis 14:18-23.Genesis 14 introduces this connection in the account and demonstration of the character of Abraham. The patriarch clearly showed his relationship and attitude to God.

When we look at the introduction of Melchizedek, "priest of the most high God." (Genesis 14:18) he blessed Abram declaring him "possessor of heaven and earth."
¹⁹ Note that he went on saying "And blessed be the most high God"
²⁰ Melchizedek king of Salem (Peace) brought forth bread and wine. (18). Note, if you will
1. This priest brought the elements of communion,
2. Abram (later named Abraham) gave a tenth of the spoils of battle and
3. The priest declared Abram as possessor of heaven and earth!

In the New Testament book of Hebrews, chapter 7 teaches us about the significance of giving of tithes (or a tenth of the spoils) which Abraham gave the priest of the most high God, Melchizedek.
This priest is described for our understanding as "King of righteousness, and after that also King of Salem, which is, King of peace."
(2). Jesus is a priest forever, after the order of Melchizedek, King of Salem, King of Righteousness, and King of Peace. The passages prior to this chapter about
Melchizedek tell about Abraham's faith and blessings pointing to the 'heirs of promise', who will"inherit the promises" as the patriarch did as these heirs imitate him.

This theme is explained in Hebrews for us to understand that Jesus as our High Priest, called after the order of Melchizedek, ministers as a priest on our behalf today. He is at the same time, King of Kings and Lord of Lords. Jesus celebrated "Communion" with his disciples, an example whereby we remember His body broken for us and His blood poured out for us and indeed for the whole world.

This is discussed elsewhere on this website.
The connection between sharing communion elements and tithing by pointing to the most high priest, Melchizedek, is in both the old and new testaments of the bible. (Genesis 14 and Hebrews 6 and 7). The significance, it seems, should not be missed that with the "communion" and tithing Melchizedek called Abram "possessor of heaven and earth" (Genesis 14:19). Bible students recognize the implications of covenants etc., but every Christian should easily recognize communion and tithing is about relationship to God.

The most familiar scripture about tithing and blessings is in the last book of the Old Testament, Malachi 3:10-11. Note verse 7 entreating God's people to return to Him demonstrating our Father in Heaven is looking for a relationship.