"@Madonna your speech at the Billboard Music Awards was inspiring. You're so brave & strong. Thanks for being that for us girls we need that," Gaga, 30, tweeted.
Madonna, 58, gave the emotional address while accepting the Woman of the Year Award at the December 9 event.
"Thank you for acknowledging my ability to continue my career for 34 years in the face of blatant misogyny, sexism, constant bullying and relentless abuse," she said.
"When I first moved to New York, I was a teenager, it was 1979, and New York was a very scary place. In the first year, I was held up at gunpoint, raped on a rooftop with a knife digging into my throat, and I had my apartment broken into and robbed so many times I just stopped bolting the door."
The two ladies were first pitted against each other when Gaga released "Born This Way" in 2011, and it sounded similar to Madonna's 1989 song "Express Yourself" and Madonna called it a blatant rip off.