1 Corinthians 16

The Lord commanded both the ancient Jews and Nephites -

"Bring ye all the tithes into the storehouse, that there may be meat in my house..." (Book of Mormon | 3 Nephi 24:10)

In modern day, the Lord again commanded -

"VERILY, thus saith the Lord, I require all their surplus property to be put into the hands of the bishop of my church in Zion,
2 For the building of mine house, and for the laying of the foundation of Zion and for the priesthood, and for the debts of the Presidency of my Church.
3 And this shall be the beginning of the tithing of my people.
4 And after that, those who have thus been tithed shall pay one-tenth of all their interest annually; and this shall be a standing law unto them forever, for my holy priesthood, saith the Lord." (Doctrine and Covenants | Section 119:1 - 4)

This same principle was taught in the days of Paul and he wrote the saints in Corinth -

"NOW concerning the collection for the saints, as I have given order to the churches of Galatia, even so do ye.
2 Upon the first day of the week let every one of you lay by him in store, as God hath prospered him, that there be no gatherings when I come.
3 And when I come, whomsoever ye shall approve by your letters, them will I send to bring your liberality unto Jerusalem." (New Testament | 1 Corinthians 16:1 - 3)

It appears that it has always been given for the priesthood leadership to administer these donations.