Gil tried to step down twice before but Silva had persuaded him to stay. This time the president accepted his resignation.
"I am leaving the government to dedicate more time to my artistic endeavors and to my family, which is growing with the addition of a new grandchild," Gil, 66, told a news conference.
He said his one complaint from his time in government is that "the ministry did not get the generous budget it deserved."
Since his appointment as culture minister, Gil - who underwent surgery for the removal of two cysts on his vocal cords last October - has divided his time between the political and musical spheres.
Gil and longtime friend Caetano Veloso are credited with inventing the Tropicalism movement, a blend of rock and bossa nova.
Tropicalism eventually influenced such musicians as David Byrne, Paul Simon and Beck, but the political content of its lyrics offended the nation's 1964-1985 military dictatorship. Both Gil and Veloso were jailed in 1968 and lived in exile in London from 1969 to 1972.
Gil has sold millions of records over his 45-year career, and won a Grammy in 1998 for best world music album.
Culture Ministry Executive Secretary Juca Ferreira has been appointed acting culture minister and is expected to be named to the post permanently in early August after Silva returns from the Beijing Olympics.
