See מעשר כספים on the Hebrew Wikipedia.
The earliest sources for giving away 1/10th of one's profits is from Avraham and Yaakov.
Avraham, as it says (Breishit 14:20):
וַיִּתֶּן־ל֥וֹ מַעֲשֵׂ֖ר מִכֹּֽל׃
Yaakov, as it says (28:22):
וְכֹל֙ אֲשֶׁ֣ר תִּתֶּן־לִ֔י עַשֵּׂ֖ר אֲעַשְּׂרֶ֥נּוּ לָֽךְ׃
Another source is from Devarim 14:22 - עשר תעשר. Tosfot on Taanit 9a quotes Sifrei:
עשר תעשר את כל תבואת זרעך היוצא השדה שנה שנה אין לי אלא תבואת זרעך שחייב במעשר רבית ופרקמטיא וכל שאר רווחים מנין ת"ל את כל דהוה מצי למימר את תבואתך מאי כל לרבות רבית ופרקמטיא וכל דבר שמרויח בו
We learn from the extra word כל, all, that it applies to all income, not just fruits.
The Bach apparently says that while giving maaser is a "midat chasidut", a good thing, it is not halacha. (Source is given as Yoreh Deah 331. I don't have it with mefarshim, so i can't confirm.) The Taz states that it is actually a mitzvah d'oraita as part of maaser ani. Others (Tzitz Eliezer 9:1) say that it's only d'rabanan.
Rambam (Hilchot Matanot Aniyim 7:5) says that giving 1/10th is the middle ground as for how much money to give.
This site deals with this here:
It is clear that the verse is referring to the mitzvah of tithing produce that grows in the ground. What about tithing other forms of income and giving it to tzedaka? While there is a mitzvah to tithe this type of earning too, does the same guarantee .of reward, and permission to test Hashem, apply to maaser kesafim, as well.
The Shulchan Aruch (Yoreh De’ah, 247:4) implies that it does. He first says that it applies to any form of giving charity, and then he quotes an opinion that it applies only to maaser, which seems to imply that the contemporary practice of maaser kesafim is also included in this.
There are those (see Pischei Teshuvah, Y. D., 247:2) who question this, and hold that it applies only to tithing produce, and not to other forms of charity. According to this approach maaser kesafim is not really a tithe, but rather, simply a method for .calculating and distributing charity
This difference of opinion would seem to be rooted in the question of what the source for tithing income other than produce really is. Some hold that it is an obligation from the Torah
(Tosefos to Taanis 9a quoting Sifri; Shaar Ephraim, 84), while others hold that it is an obligation miderabbanan (see Chavos Yair, 224; Teshuvah Me’ahavah, I:86). A third opinion (Bach, Y D., 331; this seems to be the consensus of the later poskim – see She’elas Yaavetz, I:1,3,6) holds that maaser kesafim is actually not an obligation but rather merely a custom. This dispute has a number of ramifications, and one of them would seem to be the point that we mentioned previously. If the obligation of Maaser kesafim is min HaTorah then it might be included in the permissibility to test Hashem, like other forms of maaser, whereas if is merely a method of separating funds to be distributed to charity, it might not be included in this special dispensation.
However, Ahavas Chessed (18) proves that even if Maaser kesafim is only miderabbanan, it would still be included in the special dispensation to test Hashem. This is apparent from the fact that the navi Malachi, who declared that it is permitted to test Hashem with the mitzvah of maaser, lived at the period of beginning of the second Beis Hamikdash. According to the Gemora
(Yevamos 82b) the mitzvah of tithing produce did not apply min haTorah at that time. As such, when Malachi taught that the prohibition of testing Hashem does not apply to maaser, it must have been a reference to the mitzvah of “,tithing all forms of income. In fact, implies the Ahavas Chessed, since the verse says, “and there will be food in My house the main point seems to be providing for the poor in general, and Torah scholars in particular, as they are those who reside in “Hashem’s house.” In that case, the verse in Malachi would even apply to the general mitzvah of charity, and not only maaser kesafim. Indeed, the consensus of the later authorities appears to be that one may indeed apply ,this test to any type of tzedaka (Radvaz, Matnos Aniyim, 7:10; Maharsha Pesachim 8a; Chasam Sofer, ibid; Aruch Hashulchan), as per the first opinion.