The 26-year-old signed a four-year deal with the Brazilian Serie A club on Wednesday, almost four months after parting ways with Real Madrid by mutual consent, reports Xinhua news agency.
"It makes me very proud and gives me enormous satisfaction to accept this challenge," Silva said in a social media post. "I'm thankful for the faith shown in me and let there be no doubt that I'm going to give everything I've got for Gremio."
Silva rose to prominence by helping Cruzeiro win back-to-back Brazilian Serie A titles in 2013 and 2014. He was signed by Real Madrid in January 2015, but made only eight appearances for Los Blancos before being loaned out to Marseille.
The Brazilian was due to move to Sporting Lisbon in July 2016, but a deal fell through when a routine medical exam detected a heart problem.
After more than six months on the sidelines and having been cleared of any serious health concerns, he rejoined Cruzeiro on loan and helped the club win consecutive Copa do Brasil titles in 2017 and 2018.
Silva is Gremio's second signing of the Brazilian summer to date. The Porto Alegre club last month secured right-back Victor Ferraz on a two-year deal from Santos.
Silva will join the core group on January 8.
( With inputs from IANS )