"Like Jeremiah (1:1) and Ezekiel (1:3), Zechariah was not only a prophet (1:1) but also a priest. He was born in Babylonia and was among those who returned to Judah in 538 B.C. under the leadership of Zerubbabel and Joshua (his grandfather Iddo is named among the returnees in Ne 12:4). At a later time, when Joiakim was high priest, Zechariah apparently succeeded Iddo (1:1, 7) as head of that priestly family (Ne 12:10-16). Since the grandson succeeded the grandfather, it has been suggested that the father (Berekiah, 1:1, 7) died at an early age.
"Zechariah was a contemporary of Haggai (Ezr 5:1; 6:14) but continued his ministry long after him (compare 1:1 and 7:1 with Hag 1:1; see also Ne 12:1-16). His young age (see 2:4) in the early period of his ministry makes it possible that he ministered even into the reign of Artaxerxes I (465-424 B.C.)." (THE NIV STUDY BIBLE NOTES, Introduction to Zechariah, author and unity)