"It's a great honor for me to be here today to talk about a man I have so much regard for, so much reverence for -- with whom I've done battle for 33 years… and have enjoyed every minute of it," Hatch said.
Hatch talked about running for office in Utah by saying that he would be running against Ted Kennedy.
"As a Republican coming from Utah, I stated many times on the campaign trail that I planned to come to Washington to fight Ted Kennedy," Hatch said.
"When I came to Washington, I hadn't the slightest idea that I would eventually have a strong working relationship with, and love for the man that I came to fight," Hatch added. "If you have told me that he would have become one of my closest friends in the world I probably would have suggested that you need professional help… But that's exactly what happened."
CBSNews.com Special Report: Ted Kennedy
CBS News Special Report: Ted Kennedy - The Last Brother
"I miss fighting in public and joking with him in the background. I miss all the things we could do together," Hatch added, as he told stories of their years in the Senate together.
Hatch concluded his remarks with a poem he wrote to his friend, which you can watch in the video above.
He ended with this: "I will miss my Irish friend. God be with you, until we meet again."
Read more on tonight's memorial service on CBSNews.com:
Family, Political Luminaries Honor Kennedy
Caroline Kennedy: We Have to Do What He Would Have Done
Biden: Kennedy's Legacy Is How We Look at One Another
McCain: Senate "Won't Be the Same" Without Kennedy
Kerry: Kennedy's Gift Was "Incomparable Love of Life"
Hatch: Kennedy and I Were Like "Fighting Brothers"
Dodd: "Teddy Changed Our America"
Rep. Joseph Kennedy: Teddy Was Always There
Photos: The Scene at the JFK Library Memorial
Photos: Speakers Pay Tribute to Kennedy