The following article is an adaption of the article “Copying conditions for TeX Live” (reference given at the end).
To the best of our knowledge, all software in the MiKTeX distribution is freely redistributable (libre, that is, not necessarily gratis), within the Free Software Foundation's definition and the Debian Free Software Guidelines. Where the two conflict, we generally follow the FSF. If you find any non-free files included, please contact us (reference given at the end).
That said, MiKTeX has neither a single copyright holder nor a single license covering its entire contents, since it is a collection of many independent packages. Therefore, you may copy, modify, and/or redistribute software from MiKTeX only if you comply with the requirements placed thereon by the owners of the respective packages.
To most easily learn these requirements, we suggest checking the MiKTeX package catalogue (reference given at the end). Of course the legal statements within the packages themselves are the final authority.
In general, you may redistribute MiKTeX, with or without modification, for profit or not, according to the usual free software tenets. Here are some general guidelines for doing this:
If you make any changes to the MiKTeX distribution or any package it contains, besides complying with any licensing requirements, you must prominently mention such changes in your modified distribution so that users do not take your work for ours, and know to contact you, not us, in case of questions or problems.
Especially (but not necessarily) if changes or additions are made, we recommend a clearly different title, such as “Your work, based on MiKTeX x.y.zzzz”, where x.y.zzzz is the Git tag of the MiKTeX version you are using. This credits both our work and yours.
You absolutely may not place your own copyright on the entire distribution, since it is not your work. Statements such as “all rights reserved” and “may not be reproduced” are especially reprehensible, since they are antithetical to the free software principles under which MiKTeX is produced.
You may use any cover or media label designs that you wish. Such packaging and marketing details are not covered by any MiKTeX license.
Finally, we make the following requests (not legal requirements):
a. Acknowledging that the MiKTeX distribution is developed as a joint effort by all TeX user groups, and encouraging the user/reader to join their user group of choice, as listed on the web page http://www.tug.org/usergroups.html.
b. Referencing the MiKTeX project page: https://miktex.org/.
Such information may be placed on the label of your media, your cover, and/or in accompanying text (for instance, in the acknowledgements section of a book).
Finally, although it is certainly not a requirement, we'd like to invite any redistributors to make a donation to the project, whether cash or in-kind, for example via https://miktex.org/giveback. Thanks.
MiKTeX project contact form: https://miktex.org/email/
MiKTeX package catalogue: https://miktex.org/packages/
Copying conditions for TeX Live: http://tug.org/texlive/LICENSE.TL
The FSF's free software definition: https://www.gnu.org/philosophy/free-sw.html
Debian Free Software Guidelines: https://www.debian.org/intro/free
FSF commentary on existing licenses: https://www.gnu.org/licenses/license-list.html