A celebrated textbook on enzyme kinetics is
Fundamentals of Enzyme Kinetics by Athel Cornish-Bowden, Fourth Edition, 2012, Wiley-VCH, Weinheim.
As a sample, one can download the first chapter for free, which intersperses historical references with a discussion of the basic principles of enzyme kinetics.
From that chapter, I think this paragraph is most relevant to the question:
Chemical kinetics as a science began in the middle of the 19th century, when Wilhelmy was apparently the first to recognize that the rate at which a chemical reaction proceeds follows definite laws, but although his work paved the way for the law of mass action of Waage and Guldberg, it attracted little
attention until it was taken up by Ostwald towards the end of the century, as discussed by Laidler. Wilhelmy realized that chemical rates depended on the concentrations of the reactants, but before considering some examples we need to examine how chemical reactions can be classified.
L. F. Wilhelmy (1850) “Über das Gesetz, nach welchem die Einwirkung der Säuren auf Rohrzucker stattfindet” Poggendorff’s Annalen der Physik und Chemie 81, 413–433, 499–526, https://doi.org/10.1002/andp.18501571203
P. Waage and C. M. Guldberg (1864) “Studier over Affiniteten” Forhandlinger: Videnskabs-Selskabet i Christiana, 35–40, 111-120. There is an English translation by H. I. Abrash at http://chimie.scola.ac-paris.fr/sitedechimie/hist_chi/text_origin/guldberg_waage/Concerning-Affinity.htm [The link is dead when I'm posting this, this one works: http://www.chemteam.info/Chem-History/Concerning-Affinity.html ]
K. J. Laidler (1993) The World of Physical Chemistry, pages 232–289, Oxford University Press, Oxford