Tithing was indeed part of the Mosaic Law. The word “tithe” just means “a tenth”. Numbers 18 states how Aaron, a Levite, was the first person to be in charge of all tithes that come in from the Israelites. But here’s an important pair of verses:
“(20) And the Lord spake unto Aaron, Thou shalt have no inheritance in their land, neither shalt thou have any part among them: I am thy part and thine inheritance among the children of Israel. (21) And, behold, I have given the children of Levi all the tenth in Israel for an inheritance, for their service which they serve, even the service of the tabernacle of the congregation.”
All the other tribes in Israel received a portion on land, but the Levites didn’t. Instead, the Levites were given the tithes to live on from the rest of the Israelites.
God takes tithing rather seriously. Malachi 3:8-12, KJV:
“(8) Will a man rob God? Yet ye have robbed me. But ye say, Wherein have we robbed thee? In tithes and offerings. (9) Ye are cursed with a curse: for ye have robbed me, even this whole nation. (10) Bring ye all the tithes into the storehouse, that there may be meat in mine house, and prove me now herewith, saith the Lord of hosts, if I will not open you the windows of heaven, and pour you out a blessing, that there shall not be room enough to receive it. (11) And I will rebuke the devourer for your sakes, and he shall not destroy the fruits of your ground; neither shall your vine cast her fruit before the time in the field, saith the Lord of hosts. (12) And all nations shall call you blessed: for ye shall be a deslightsome land, saith the Lord of hosts.”
It’s not every day that you head God say, “Test me”, but He just did in the above passage. In return for giving a tithe to God, He will bless us in abundance.
I don’t think the New Testament had anything against tithes, or even mention it really, but I’m not the most knowledgeable about the NT. As far as I know, we are still called to give at least one tenth of what we make to God.