Sartain said a date for his retirement would be determined later this year.
Seattle also has two auxiliaries, Bishops Eusebio Elizondo and Daniel H Mueggenborg.
Etienne, 59, served as a priest of the Archdiocese of Indianapolis from 1992 until 2009, when he was appointed Bishop of Cheyenne, Wyoming.
In 2016, Pope Francis named him to head the Archdiocese of Anchorage, Alaska.
Etienne wrote in a blog post April 29 that he is excited and surprised by the announcement of his new appointment, and noted that his time as head of the Anchorage archdiocese the last two and a half years was "too short."
"But I am mindful of a phrase in Sacred Scripture that refers to God's timing, known as 'the fullness of time,'" he wrote. "That time has now come in God's plan for new leadership" in Anchorage.
The archbishop said he has known Archbishop Sartain for many years, and has nothing but "admiration and esteem" for him, and that he has been praying for the people of Seattle and western Washington since receiving the news of his appointment April 13.
He also expressed his gratitude for the "profound faith" of the people of Anchorage: "We now place the future once again, as always, into the hands of a faithful and loving God," he said.
Archbishop Etienne's Rite of Reception in Seattle is scheduled for Friday, June 7.
Etienne, an outdoorsman, grew up as one of six children. He has two brothers who are priests and a sister who is a religious sister.
He graduated from the University of St. Thomas/St. John Vianney College Seminary in St. Paul, Minnesota, with a degree in business administration before studying at the Pontifical Gregorian University in Rome.
After serving as an associate pastor and assistant vocations director in Indianapolis for a period, he returned to Rome to receive his licenciate in spiritual theology.
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In the U.S., he later served as vocations director in the Archdiocese of Indianapolis, vice-rector of the Bishop Simon Brute College Seminary in Indianapolis, and as a parish priest.
He was appointed Bishop of Cheyenne in 2009. He has served as a metropolitan, the Archbishop of Anchorage, since November 2016.
The Archdiocese of Seattle covers the western part of Washington state, from the Canadian to the Oregon border and from the Cascade Mountains to the Pacific Ocean.
It has 173 parishes, missions, and pastoral centers and serves over 579,500 Catholics.
Reflecting on the fact the announcement of his appointment was made on the feast of St. Catherine of Siena, Etienne said he is mindful of her and her "profound love for God the Father, for her Lord, Jesus Christ, for the Holy Father and for the Church."
"For many years, I have seen St. Catherine as a companion and a kindred spirit," he said. "She called the Holy Father 'Sweet Christ on earth.' She was his emissary on various occasions, and she offered many sacrifices for the unity of the Church."