Adams, the show's original anchor, will be back in the presenter's chair and will share the role with Carol Vorderman and Andrea McLean.
Nolan will return to a seat on the panel on Monday, October 7.
Kaye left the show in 2006, while Nolan departed in 2011 with an emotional send-off.
The duo join a lineup of panelists, which includes Sherrie Hewson, Jane McDonald, Denise Welch, Lisa Maxwell, Janet Street-Porter, Sally Lindsay, Linda Robson and Shobna Gulati.
"After two and half years away, now feels like the right time to 'come home' to Loose Women," said Nolan.
"I'm ready to embrace the show whole-heartedly again and return to the most special of places - the homes of our viewers. It's the public that have always mattered the most to me and the Loose Women audience are the most loyal of all.
"They have been so supportive to my family during the devastating loss of our beautiful sister and I hope they'll be as pleased to have me back as I am to be back."
Adams added: "I felt privileged to have been one of the original Loose Women and now feel doubly privileged to be invited back six years on.
"Loose Women is perhaps the only show on which you can be unapologetically female... smart, sassy, sometimes stroppy, sometimes silly but always straight talking.
"It's the world and what matters in it through a female prism, a perspective we don't see or hear enough of, and I can't wait to play my part again."