Monson was "strong and clear," the trio said at a news conference later Saturday, and the man considered a "prophet, seer and revelator" in The Church of Jesus Christ of Latter-day Saints assured each one that the assignment came from God.
They were tapped to fill vacancies in the Quorum of the Twelve Apostles created by the recent deaths of L. Tom Perry, Boyd K. Packer and Richard G. Scott.
Despite endless predictions and pleading in some Mormon circles for non-Americans, men of color, or those outside the church's employ to be picked, no historic choices emerged.
All three new apostles were born in Utah to Mormon parents. They are Anglos and have spent considerable time in church service.
Rasband was the senior member of the Presidency of the Seventy, the third highest tier of Mormon authorities. Stevenson was and still is, for now the church's presiding bishop, overseeing the global faith's vast real-estate holdings, business interests and humanitarian efforts. Renlund, a former cardiologist, was a member of the First Quorum of the Seventy.
Independent LDS demographer Matt Martinich was not surprised by the selections.
"General authorities are almost entirely Caucasians," he said. "I bet we will see a non-white apostle once we have more non-white general authorities."
In late 1996, 83.5 percent of top Mormon officials were born in the United States, he noted. That percentage had declined to 66 percent by early 2013.
Matthew Bowman, who teaches history at Henderson State University in Arkansas and wrote "The Mormon People: The Making of an American Faith," echoed that sentiment.
"These picks reflect the same institutionally conservative procedure normally followed," Bowman said, "mid-level leaders with long experience elevated in rank."
Still, Bowman believes one day there will be an apostle from the global south, where so many Latter-day Saints live.
"The church needs that perspective," Bowman said, "as its center of gravity shifts to that region and seeks to become a truly worldwide religion."
Others had hoped for more ethnic and cultural diversity in Saturday's appointments especially given the 15 million-member faith's rapid ascent in Africa, Latin America and Asia.
"Those who view the calling of new apostles as a direct revelation from God will see these new additions as the latest in a long chain of inspired succession," said Jared Tamez, co-editor of the recently released volume "Just South of Zion: The Mormons in Mexico and Its Borderlands." "Those who feel that [LDS apostle M. Russell] Ballard's words [Saturday] morning about the fallibility of church leaders extends even to decisions about apostolic succession will feel that an opportunity to see church leadership more closely reflect the face of the worldwide church has been missed."
At the news conference, the three responded to their lack of diversity.
"We're going to be apostles to everyone," Rasband said. "We are not going to be apostles to our local community or the state where we're from. We're called to bear the name of Christ throughout the world."
Marta Tobar, a Mormon from Jalisco, Mexico, in town for conference, said she was not disappointed that none of the new apostles hails from Latin America, Asia, Africa or Europe.
"They're called for a reason," said her daughter, Diana Tobar. "They've got to be good guys."
Argentina natives Raul and Teresa Dominguez, who live in West Jordan, said they were happy with the men called, because they were chosen by the Mormon president.
"The prophet is the servant of the Lord," Raul Dominguez said.
How will the new apostles resist the adulation that often comes with such a high position, showing the Mormon faithful that they can be shepherds and servants rather than bosses and CEOs?
"As I think about this sacred calling, I think it is more leading by serving, not serving by leading," Stevenson said. "Jesus Christ considered himself a servant, and we, too, consider ourselves servants."
Remembering your roots will help, Rasband said. "In my case, I was born to a Wonder Bread truck driver and a dear mother who tried her very hardest to stay at home and raise a family."
These days, he said, "I have a wife who is going to help me be well grounded and not suffer from that malady."
Renlund, who labored for LDS Church in southern Africa for six years, said what keeps him humble is "seeing people in different circumstances and seeing them through Heavenly Father's eyes."
Viewing all members in that way "changes us," he said, "[by] recognizing and feeling the compassion the Savior has for them."
Utahn Neylan McBaine, author of "Women at Church: Magnifying LDS Women's Local Impact," was pleased to see a reflection of her own experience as the only child of a professional mother in Saturday's selections.
"The Renlunds specifically bring a different kind of experience to the quorum," McBaine said, "especially the influence of his wife, Ruth, who has had a highly successful legal career, and they only have one child."
Monson attended all of Saturday's sessions, but Henry B. Eyring, his first counselor in the governing First Presidency, announced the new apostles.
And now that they have been sustained by Mormons around the globe though there was a smattering of no votes in the Conference Center for the top LDS leaders they will be ordained this week, according to an LDS Church news release.
The three will hold their new jobs for the rest of their lives.
Kristen Moulton and David Noyce contributed to this story.