McDaniel was elected unanimously to replace Terri Lynn Land, who resigned on announcing her campaign for the U.S. Senate, and will serve through the rest of Land's term until August 2016.
"The result shows that we do have unity in our party," McDaniel told the Free Press. "We have a mission, and we are united in our goal to elect our Republican leaders."
McDaniel worked on Mitt Romney's campaign in Michigan, and has also worked as a GOP activist and in the private sector.
She would not address Agema's controversial remarks or his refusal to resign.
"I'm not getting into that," McDaniel told reporters. "He's been asked to resign. He's decided not to do so. I'm moving forward."
Multiple Michigan Republicans and GOP U.S. representatives have called on Agema to step down, and other members of the party have condemned his comments.
Agema last year compared being gay to alcoholism. And in January, he posted a comment on Facebook asking, "Have you ever seen a Muslim do anything that contributes positively to the American way of life?"