Brigham Young was ordained an Apostle on February 14, 1835 under
the hands of the Three Witnesses; Oliver Cowdry, David Whitmer, and
Martin Harris.
The Three Witnesses were called by revelation to choose the
Twelve Apostles and were "blessed by the laying of the the hands of
the First Presidency" (Joseph Smith, Jr., Sidney Rigdon, and
Frederick G. Williams) to ordain the Twelve Apostles (see Church
History Vol 2 page 187)
Joseph Smith, Jr. and Oliver Cowdry received the Melchizedek
Priesthood in 1829 under the hands of Peter, James, and John. They
were visited by Peter, James, and John who were sent as resurrected
beings to restore the Priesthood authority to the earth. (See
Doctrine and Covenants 21:12-13)
Peter, James, and John were ordained Apostles by the Lord Jesus
Christ. (See John 15:16)
Brigham Young was ordained an Elder on the date of his baptism,
April 14, 1832 by Eleazer Miller, however, Priesthood lines of
authority are counted from the highest office of priesthood
received, so the line of authority extending from Elder Miller is
insignificant.