The Soda Stereo star suffered a stroke and slipped into a coma in May, 2010. He never regained consciousness.
Cerati became one of the world's biggest Spanish-language rock stars and helped to nurture young talent, like Shakira, who performed with him at the Latin Grammy Awards in 2008.
Paying her respects to her friend on Twitter.com, the pregnant singer wrote, "Gustavo, our most important song is yet to be written. I love you, my friend. And I know you love me."
Martin also offered his thoughts on Twitter.com, adding a simple, "RIP Gustavo Cerati."
Enrique Bunbury, Juanes and Julieta Venegas also paid tribute to the singer/songwriter on Twitter.com, while fans started gathering outside the clinic where the Latin Grammy Awards winner died on Thursday morning to leave floral tributes and messages.