Hatch, a Republican from Utah, worked closely with his liberal colleague from Massachusetts on a number of pieces of legislation. He notes on his YouTube page that the song is called "Headed Home" and that he wrote it with songwriter Phil Springer.
"Take a moment to listen to the words," Hatch writes. "You don't have to agree with everyone's politics...none of us agree 100 percent of the time. But you have to admire a lifetime dedicated to public service and improving the lives of others -- and that is just one of the many things that made Ted great. I think this song captures a small part of Ted's legacy of service."
Hatch and Springer wrote the song last year, and it is performed by baritone Tony Middleton.
"Through the rain and fog," Middleton sings, "We can find a clear day, shoo the shadows and doubts away, and touch the legacy that is ours."
In a separate statement he released today, Hatch noted some of the legislative achievements he and Kennedy accomplished together, including Ryan White AIDS Act, which established a federally funded program for people living with HIV/AIDS; the State Children's Health Insurance Program; the Americans with Disabilities Act; and the FDA Modernization Act of 1997.
"When I first came to the United States Senate I was filled with conservative fire in my belly and an itch to take on any and everyone who stood in my way, including Ted Kennedy," Hatch said in his statement. "As I began working within the confines of my office I soon found out that while we almost always disagreed on most issues, once in a while we could actually get together and find the common ground, which is essential in passing legislation."
Hatch was one of the few Republicans working on creating a bipartisan compromise for health care reform, but he last month he abandoned the talks, which include a few of his fellow Senate Finance Committee members.
Read more on the life and death of Sen. Edward "Ted" Kennedy: