Brokaw, 74, stepped down as anchor in December 2004 but has remained with the network as a special correspondent, currently covering the Winter Olympics coverage in Sochi, and has continued to work on NBC projects during his treatment, NBC News said in a statement.
It said Brokaw and his physicians were "very encouraged with the progress he is making."
In his own statement accompanying the network announcement, Brokaw said: "With the exceptional support of my family, medical team and friends, I am very optimistic about the future and look forward to continuing my life, my work and adventures still to come."
He added, "I remain the luckiest guy I know."
A South Dakota native who joined NBC in 1966, Brokaw served as White House correspondent during the Watergate scandal of the Richard Nixon administration and hosted NBC's "Today" show from 1976 until 1982.
He replaced John Chancellor at the helm of the "Nightly News" desk, first as co-anchor that year with Roger Mudd and then as sole anchor in September 1983, while the "CBS Evening News with Walter Cronkite" was still the top weeknight network newscast.
Within several years, however, Brokaw and "Nightly News" moved to the top of the Nielsen ratings, leading Dan Rather and the "CBS Evening News" and Peter Jennings' "ABC World News Tonight" through the end of Brokaw's tenure in 2004.
The youngest of his Big-Three network news contemporaries, Brokaw was the first to retire as anchor, stepping down from the job at age 64.
Despite his accomplishments as a journalist, Brokaw has said it was a work of history that he was most proud of—his book "The Greatest Generation," a bestseller about Americans who grew up during the Great Depression and served in World War Two.
Multiple myeloma is a cancer that strikes white blood cells in the bone marrow called plasma cells, which normally produce antibodies to help fight infection. But in multiple myeloma, an over-abundance of malignant plasma cells releases unhealthy levels of a protein into the bones and blood that in turn can cause damage to bone tissue and organs.
There is no cure, but treatments are available that slow its progression, according to the medical website WebMD.com. —Reuters
