"V'achalta v'savata u'veirachta es Hashem Elokecha 'al ha'aretz hatovah 'asher nasan lach" - "and you shall eat and be satisfied and bless Hashem, your G-d, for the good land which he has given you" (Eikev 8:10). This passage serves as the Biblical source for the commandment to bless Hashem after a meal. (Bread must be consumed to be obligated min haTorah due to the proximity of the passage "a land in which you will eat bread unsparingly" (verse 9) to this passage (see B'rachot 44a). Some rishonim maintain that even the B'racha Mei'ein Shalosh recited after other foods made from grain and after fruit of the Seven Species is also Biblical in nature (see Mishna B'rura to O.C. 209:10).) Although the overwhelming majority of blessings, such as those before eating food and before performing mitzvot, are Rabbinic in origin, Birchas HaMazon is Min HaTorah. Ramban (Hashmatos l'Mitzvos 'Asei 15) and other rishonim maintain that the blessing before Torah study is also of Biblical origin and is derived from the verse "ki sheim Hashem ekra, havu go'del lailokeinu" -- "when I call out the name of Hashem, give praise to our G-d" (Ha'azinu 32:3).
However, on a Torah level, a blessing need be recited only after eating food but, by contrast, it is recited before engaging in Torah study. Chazal (our Rabbis) instituted additional blessings before eating bread (and other foods) as well as a blessing after reading the Torah in public. Meshech Chachma suggests a fascinating rationale for the difference in placement between Birchas HaMazon and Birchot HaTorah on a Torah level. All blessings thank the Source of All for His kindness. Birchat HaMazon focuses on physical bounty whereas Birchot HaTorah focus on the spiritual endowment of Torah. With respect to this aspect of praise of G-d, both of these blessings should have been recited in the same location. However, each of these blessings also reinforces another idea, each uniquely relevant to the sphere of life it addresses. This particular theme helps explain the blessing's Biblical placement.
Eating, or more generally, partaking of material goods yielded through much hard work and energy, can lead to an attitude of haughty self-achievement, without properly recognizing that it is Hashem who has provided the physical wherewithal, the physical goods and infrastructure and the mental acumen (see Targum Onkelos to verse 18) for the production of such bounty. This danger exists primarily after partaking of the material goods, after being satisfied by them. Hence, the Torah directs us: be certain to recognize G-d as the Source of the bounty by praising Him as the "zan es hakol" and the bestower of the Land of Israel from which the food was produced. (See also Eretz Yisrael, by Rav Mayer Twersky.) The context of this commandment verifies this approach. Immediately preceding the commandment, the Torah indicates that the miracle of the forty-year daily delivery of man in the desert served to highlight to the Jewish People the fact that "Man does not live by bread alone, but through the word of G-d, does Man live" (ibid. 3) which (among other meanings) can be read as: it is not your efforts alone that bring about the bread, but, just as the manna from the sky was clearly Divinely granted, so too bread from the ground is also Divinely granted through the mask of the natural order created by G-d.[1] After the commandment to bless G-d after eating, the Torah warns us: "and lest you grow haughty and you forget G-d ... who has fed you man in the desert ... and you will say: 'my strength and the might of my hand produced this bounty.' And you shall remember Hashem, your G-d, for it is He who gives you strength to produce bounty" (ibid. 14-1).
Concerning Torah study, the opposite is true. Once having studied it, plumbed its depths, partaken of its mysteries and delights, the Torah is clearly recognizable as a Divine work, which, due to Divine beneficence, was given to Bnei Yisrael to partake of. However, before studying it, the student must be made aware of its Divine origin: that the Torah is not a wisdom like all other wisdoms, intellectually stimulating, fascinating but not directly Divine in origin. The danger exists of the Torah being utilized as a tool for personal intellectual achievement. Therefore, the learner of Torah must first recognize the Torah's source. A passage in tractate N'darim (81a) attributes the destruction of the Beis HaMikdash to the omission of the blessing on the Torah. Some commentaries (see Ran and Bach (on Tur O.C. 47)) suggest that the omission of a blessing was symptomatic of treating the Torah like any other wisdom whose study does not require a blessing. R. Chayim Volozhin in his Nefesh HaChayim (4:6-7) writes that it is advisable before and during Torah study to stop learning temporarily to contemplate that one is actually studying the Divine Word and connecting to Hashem "for He and His Will (as expressed in the Torah) are One." Some recite various tefilos before Torah study (in addition to the one mentioned in the Mishna (B'rachot 28b)) requesting that the Torah study lead to increased fear of Heaven (see standard edition of Yachin U'Boaz Mishnayot). All of these practices highlight this same theme.
From morning to evening, halacha demands of its adherents to constantly praise G-d through blessings: on waking up, on walking, on seeing, on eating, on drinking, on bodily functions, on learning, on mitzvot. Indeed, Chazal legislated the recital of a minimum of 100 blessings a day (see Shulchan Aruch 46:3). The triple themes of praise to G-d for providing for our spiritual and physical needs, recognition that it is He alone Who allows us to succeed, and appreciation of the ultimate sanctity of the greatest of His gifts to us - His wisdom as contained in the Torah which He has allowed us to enjoy - should guide us throughout our engagement in both the spiritual and physical aspects of existence.
[1] This particular point is an addition to Meshech Chachma's words.