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The band said in a statement that Springsteen, Gaga and The Black Keys, who span the American rock and pop genres, will join them at their last performance in Newark, New Jersey.
"Now the fun begins of trying to figure out the best songs to perform together," the statement said.
Lady Gaga, 26, tweeted her excitement.
"He had me at 'hello, it's Mick'."
British rockers The Rolling Stones -- Mick Jagger, drummer Charlie Watts and guitarists Keith Richards and Ronnie Wood -- began a series of five anniversary concerts on November 25, two in London and three in the United States.
They will also play at a benefit concert in New York on Wednesday for victims of Hurricane Sandy, which hit the northeastern United States in late October.