The seven-time Tour de France champion and the rock star announced their engagement in September. It would have been her first marriage and his second. He has three children from a previous marriage.
"After much thought and consideration we have made a very tough decision to split up. We both have a deep love and respect for each other and we ask that everyone respect our privacy during this very difficult time," the statement said.
Armstrong, 34, recovered from testicular cancer that had spread to his lungs and brain to become the dominant athlete in one of the world's most grueling sporting events.
His seven consecutive Tour de France titles from 1999 to 2005 are a race record. He retired after winning his last race with Crow rooting him on.
Armstrong and the 43-year-old Crow met in October 2003 and began dating shortly after.
Crow called Armstrong the inspiration for her last album, "Wildflower," which was released in September.
She performed a free concert soon after in Austin, Armstrong's adopted hometown, to coincide with the ninth anniversary of Armstrong's diagnosis with testicular cancer.
"We've always had parties or celebrations on that day," Armstrong said in late September. "It was just a way to do something for a city that has done a lot of things for me. We're basically saying thank you for all the support."
Crow talked about being part of a celebrity couple in an interview with The Associated Press in November, saying she wasn't crazy about all the attention that goes with it.
She said celebrity magazines are more interested in seeing a couple break up than reporting on them being happy together.
"When we were rumored to have split, and when our publicists called these magazines to say we haven't split, the magazines were all so disappointed because that's really what's selling, rooting for a couple and then they split," she said. "That's what sells the magazines.
"Why can't we just report things the way they are or see things for the good in them? ... It's an insidious energy."
Armstrong was living with Crow on a ranch in the Austin area.