It seems that it is from the Rishonim. Rabbeinu Yonah in Sefer HaYirah says:
תמיד הרגל על שפתיך דברי יראת שמים כגון הוי עז כנמר. סוף דבר הכל נשמע (קהלת יב). ועתה ישראל מה ה' אלהיך שואל מעמך כי אם ליראה וגו' (דברים י). מאד מאד הוי שפל רוח. וכיוצא באלה הרגל על לשונך ואז לא תכשל.
Always accustom your lips (to) words of the fear of Heaven such as, "Be strong as a leopard, [" (M. Avot 5:24); "The end of the matter, when all is said and done: [Fear God and keep His commandments]," (Eccl. 12:13); "And now, Israel, what does the Lord your God require of you but to fear [the Lord your God]," (Deut. 10:12); "Be very, very humble," (M. Avot 4:4). And such as come out like these, accustom your language, and you shall not come to grief
The Artscroll Siddur brings a Sefer Yereim that says to say both of these parshios each day. I haven’t been able to find it inside though.