Bundesliga strugglers Borussia Dortmund have agreed to sign Slovenia international Kevin Kampl in January.
Cardiff have agreed to sell Norwegian midfielder Mats Daehli to Freiburg in January.
The new deal means the 28-year-old Brazilian is tied to the Ligue 1 club until June 2018, ending the speculation surrounding his future after he was heavily linked with a move to Barcelona earlier this summer.
"We are very proud to have extended with Thiago, an exemplary player both on and off the pitch," club president Nasser Al-Khelaifi said in a statement.
"He symbolises PSG's wish to build one of the most successful teams in Europe in the mean time."
Silva joined PSG in July last year from AC Milan and made 22 appearances in last season's title-winning campaign.