There were several proposals for Reconstruction Amendments as the Civil War drew to a close, including the formal constitutional abolition of slavery. The Thirteenth Amendment was a bit of a group effort, largely involving the Senate Judiciary Committee. Senator John B. Henderson submitted a joint resolution to have the committee consider a constitutional amendment for abolition, kicking things off. Representatives James Mitchell Ashley and James F. Wilson offered some of the earlier versions. Other versions that were more expansive were proposed by Representative Thaddeus Stevens and Senator Charles Sumner.

Sumner proposed the following language on February 8, 1864:

All persons are equal before the law, so that no person can hold another as a slave; and the Congress shall have power to make all laws necessary and proper to carry this declaration into effect everywhere in the United States.

The Senate Judiciary Committee was chaired by Senator Lyman Trumbull, who wanted less expansive language and to compromise between the Radical Republicans (more liberal) and more conservative Republicans such as Lincoln who were compromise-driven. Wilson, Ashley, Henderson's proposals were incorporated into the Judiciary Committee's proposal to the Senate, which also included text from the Northwest Ordinance of 1787, which created the Northwest Territories and prohibited slavery therein. This 1787 Ordinance, specifically Article 6, is where you first see the language you refer to:

Art. 6. There shall be neither slavery nor involuntary servitude in the said territory, otherwise than in the punishment of crimes whereof the party shall have been duly convicted: Provided, always, That any person escaping into the same, from whom labor or service is lawfully claimed in any one of the original States, such fugitive may be lawfully reclaimed and conveyed to the person claiming his or her labor or service as aforesaid.

Given that the Fugitive Slave Clause was to be no more, the latter bit about fugitive slaves was obviously not included. It basically incorporated everything up to the colon.

Henderson's version included language changing the amendment procedure, allowing for a simple majority in both houses as well as ratification by 2/3 of the states, which was removed by the committee. The amendment would go through a year of opposition by Southern Democrats until the Republicans gained a mandate in both houses in 1864, making the pathway to passage easier. By January 1865, Lincoln was making personal appeals to members of Congress to get passage. It passed on January 31, 1865. Lincoln signed the amendment on February 1, 1865, though this was not really required (as confirmed by a Congressional Resolution passed on February 7). It then took until December 6, 1865 to get the amendment ratified by the states (the worst stragglers were South Carolina, Alabama, North Carolina, and Georgia, though New Hampshire, Connecticut, Arkansas, and Tennessee took their time too).

Sources (cribbing the format from Wikipedia, which conveniently also uses these sources and has many more):

Tsesis, Alexander (2004). The Thirteenth Amendment and American freedom: a legal history. New York: New York University Press. 

Vorenberg, Michael (2001). Final freedom: the Civil War, the abolition of slavery, and the Thirteenth Amendment. Cambridge: Cambridge University Press. 

"Northwest Ordinance; July 13, 1787". Avalon Project. Lillian Goldman Law Library, Yale Law School. http://avalon.law.yale.edu/18th_century/nworder.asp

"13th Amendment". Legal Information Institute. Cornell University Law School. November 20, 2012. https://www.law.cornell.edu/constitution/constitution.amendmentxiii.html

Follow on question: what is the practical effect of that text?

To follow that up, is a judge able to sentence someone to a period of slavery? If so, has any American judge ever done so?

If I could ask a follow up question:

Could anyone speak to the manner in which forced labour/prison labour was used as a tool of racial oppression after the collapse of Reconstruction? More specifically, were there people who advocated the 'chain-gang' system as an attempt to reconstitute the 'virtues' of slavery?

For additional context, prisoners (specifically felons) are not granted a number of constitutional rights (voting, owning firearms, etc).

A brief reminder for people of the rules here, namely Politics/20 Year Rule. We have removed (and likely will continue to...) several comments looking to comment on or discuss penal issues as they relate to the modern political environment. Please, keep the discussion historical. If you wish to discuss modern prison reform, consider another, more appropriate subreddit. If someone wishes to create a thread for it, I'd be happy to link it for those interested.