Manchester United manager Louis van Gaal has refused to rule out the possibility of signing goalkeeper Victor Valdes.
Manchester City boss Manuel Pellegrini says he is confident that England goalkeeper Joe Hart will sign a new contract.
The 34-year-old has agreed a two-year contract in Brazil after finding his chances limited at the Juventus Stadium since he left Inter Milan in the summer.
A statement on saopaulofc.net read: "Sao Paolo has completed the signing of Lucio.
"A world champion with the Brazilian national team in 2002, he was also captain for five years, playing 105 games and scoring four goals.
"Lucio comes to Sao Paulo in order to bring more experience to a squad that could play in up to seven competitions during 2013."
Lucio, who started his career with Internacional, won the Bundesliga three times with Bayern Munich before winning the treble under Jose Mourinho's Inter in 2010.
The defender originally saw a move to Sao Paolo fall through before he joined Juventus in July, but the Italian champions reached an agreement to rescind his contract on Monday.
Sao Paolo director of football Adalberto Baptista said: "Signing Lucio has been a long-standing dream for Sao Paulo.
"We came very close to signing him in July, but in the end it was not possible.
"This time everything went well and he will add a lot of quality, experience and leadership to the squad."