According to Reformed Theology, what is the doctrinal basis for belief in New Testament tithing? Most Reformed churches refer to "tithes and offerings" as an understanding of the giving structure in church. Reformed Theology as a theological framework is careful about ensuring there is a biblical foundation for worship (regulative principle) and has a strong emphasis on the biblical covenants and their historical administrations. Therefore, I assume there is a basis for the belief that tithing is an enduring New Testament establishment for the church.

Ideally, this would be a representative theologian (a reformer, puritan, modern reformed theologian, etc.) explaining the basis for believing that the Bible teaches the tithe as an enduring function of the church that extends beyond the Mosaic administration. 

I am specifically talking about tithing 10% of the household income as a commandment of God, not the general principle of generous giving which is immediately obvious in the New Testament.
Based on the frequency with which the word &quot;tithe&quot; is mentioned in Reformed churches, one might expect that Reformed theologians overwhelmingly believe in an obligation for giving 10%.  But in fact, many prominent Calvinists do not believe it to continue as a command, such as John Owen, Francis Turretin, and John Gill.1
Many accept the tithe as a general rule, such as John Frame, but hesitate to make it truly obligatory:

Again and again in the Old Testament the figure of 10 percent recurs.  That is the Lord's portion.  It may be that in the New Testament that amount is not strictly required.  But surely the &quot;cheerful&quot; giving of 2 Corinthians 9:7 cannot be much less than that.2

Still, there are some in the Reformed tradition who make the case for the continuation of the obligatory tithe.  Among them, unsurprisingly, are theonomists like Gary North.  He combines what theonomists are known for – seeking to re-establish OT law in modern societies – with a concept of a &quot;sovereign institutional church,&quot; and calls for churches to enforce the tithe by comparing member incomes to their donations and subjecting violators to discipline.3
But not all defenders of the modern tithe go so far.  I'll also refer to 19th-century Presbyterian minister Alexander L. Hogshead, who focuses more on New Testament passages related to tithing to make his case for the continuance of the practice.
Here are the main biblical arguments these two authors make:

The tithe precedes the mosaic law
The tithe is not abrogated in the NT, but rather assumed and implied

Tithe precedes Moses
Numerous commentators note that the first recorded instance of a tithe in the Bible precedes the giving of the Mosaic law.  Gary North argues for the modern relevance of Abraham's giving of a tithe to Melchizedek in Genesis 14:

The New Testament does not ground the tithe on the Mosaic law. On the contrary, Hebrews 7 establishes the authority of Jesus Christ's high priestly office in terms of Melchizedek's collection of the tithe from Abraham. The superiority of the New Covenant to the Old Covenant is seen in Abraham's payment of his tithe to Melchizedek – a representative judicial act of submission in the name of Israel and his son Levi. Any attempt to escape the obligation of the tithe is an assault on the New Covenant's High Priest, Jesus Christ.4

Tithe continued in the NT
Hogshead argues that God's provision for the leadership of his people has not changed – that it is found in the obligatory tithe.  He focuses first on Paul's admonishment in 1 Corinthians 9:7–14, in which Paul cites the Mosaic law in reference to the support of his ministry, and concludes:

13 Do you not know that those who are employed in the temple service get their food from the temple, and those who serve at the altar share in the sacrificial offerings? 14 In the same way, the Lord commanded that those who proclaim the gospel should get their living by the gospel. (ESV; emphasis added)

Hogshead particularly emphasizes the phrase translated &quot;in the same way,&quot; arguing that these words &quot;express Christ's positive appointment, in reference to the christian ministry, of the substantial features and principles of the old divine law.&quot;5
Against those who argue that the New Testament does not explicitly require a tithe, Hogshead argues:

A large portion of the disciples of Christ were converted Jews, who carried with them their hereditary attachment to all the essential parts of divine worship [...] These christians did not need specific instructions in relation to those duties that they had been accustomed to regard as divinely enjoined.
In relation to this branch of divine service, they knew that from the beginning, it was in part regulated by fixed laws, and in part varied by circumstances.  The tithes and first-fruits were fixed, the free-will offerings were varied according to the exegencies of the church.  The only points upon which they needed instruction were the changed circumstances in which the new dispensation placed them.6

Thus Hogshead sees a continuation of the obligatory tithe, and contends that New Testament appeals to generosity are intended &quot;to secure from christians enlarged offerings beyond the former standard&quot; but do not eliminate the obligation of that former standard – the tithe.
Similarly, he appeals to Hebrews 13:16, Galatians 6:6–7, Luke 10:7, and 2 Corinthians 11:8, arguing that with their language of &quot;wages&quot; and &quot;robbery,&quot; they would have been understood as continuing the obligatory tithe, not abrogating it.
Summary
Reformed advocates of the continuation of the tithe argue that the obligation of tithing pre-existed the Mosaic law, and that the New Testament assumes and implies its continuation today.  Thus they see it as a part of the broader Mosaic law that ought to be reestablished (i.e., theonomy), or as a part of the law that was never abrogated and thus continues.

References

David Croteau, You Mean I Don't Have to Tithe, 279
The Doctrine of the Christian Life, 801
Tithing and the Church
Ibid., 2
The Gospel Self-Supporting, 19
Ibid., 27