When did Jews adopt the custom of saying "Baruch Hashem"? The only people who said B"H in the Chumash were non-Jews: Noah, Malkitzedek, Avimelech, Eliezer, Lavan, and Yitro!
The earliest source that I can find of a Jew saying Boruch Hashem is King David. (Shmuel1 25:32).
There are also many places in Tehilim (28:6, 31:22, 41:14, 72:18, 89:53, 106:48, 124:6, 135:21, 144:1) where it says Boruch Hashem.
Ezra 7:27 also uses the terminology Boruch Hashem.
I believe the custom of saying this comes from Tractate Berachos in the Mishnah, Chapter 9 Mishnah 5: Berachos 9:5
Seems that since we should "greet eachother in the name of Hashem" we should also describe the way we are feeling using the name of Hashem. Another more simple explanation is that we should always be thankful we are alive, and thus when someone asks how we are, we answer "Baruch Hashem" (Blessed is Hashem) because we are thankful we are alive and not dead not matter how we're feeling (sick, well, etc.)