The highly-rated centre-back has seven caps for his country, and was linked with a move to the Premier League after Vasco found themselves embroiled in financial difficulty.
Liverpool boss Brendan Rodgers was thought to be a big fan of the defender, and was eyeing the 24-year-old as a potential Jamie Carragher replacement. But United and Liverpool have both lost out to Cruzeiro.
The complicated deal involves Cruzeiro purchasing a 45 per cent stake in the player following the transfer, with the remaining 55 per cent split between several third parties.
The cash-plus-players deal also involves three Cruzeiro first-teamers joining Vasco as part of the transfer. Full-back Diego Rennan and Alisson will move to the Rio-based side, while Wellington Paulista - currently on loan with Premier League side West Ham - will also move to Vasco.
The £4.7m deal is something of a coup for Cruzeiro, who've beaten several European giants to the signing of Dede. As well as Liverpool and Manchester United, Serie 'A' side AC Milan were also thought to be monitoring the centre-back.
But, with perhaps one eye on next year's World Cup on home soil, the 24-year-old has decided to snub a move to Europe and stay in Brazil.