[Math] Origin of the modern definition of the tensor product

Question

Due to whom is the modern (i.e. via its universal property) definition of the tensor product, and in which article was it communicated?

Answer 1

My recollection agrees with Mariano. Here's an except from Weibel's History of homological algebra

and from p. 172 of Mac Lane's Homology

and from Whitney's Collected Papers v. 1