Anderson confirmed the good news in an entry in her online diary: "It's been a whirlwind ... spontaneous but well thought through."
When contacted by The Associated Press, Marleah Leslie, Anderson's spokeswoman, declined to comment on the report.
Photographs posted on the Internet show Anderson, 39, and Kid Rock, 35, embracing and enjoying the sun on the coastline of France, the AP reports.
The actress and the rock star, whose real name is Bob Ritchie, became engaged in the Las Vegas desert in April 2002, but never set a wedding date.
Anderson and her first husband, Tommy Lee, divorced in 1998 after three years of marriage. They have two sons, Brandon, 10, and Dylan, 8.
"Feels like I've been stuck in a time warp," said the "Baywatch" bombshell in her cryptic diary entry. "Not able to let go of MY family picture ... it's been sad and lonely and frustrating ... I've raised my kids alone in hope of a miracle.
"Well my miracle came and went. And came back and back because he knew that I'd wake up one day and realize that I was waiting for nothing."
The United States has imposed new sanctions against the Nord Stream 2 gas pipeline project, which still remains under construction