The foward joined United from Portuguese club Guimaraes in a £7.4million deal in 2010 but did not make a single start in the Premier League.
He made just two appearances off the bench in the top flight, one FA Cup outing, two League Cup appearances and one in the Champions League.
United have confirmed that they will receive £2.4m for Bebe and are entitled to 50 per cent of any future transfer fees.
Bebe also spent time on loan back in Portugal with Rio Ave and Pacos de Ferreira and in Turkey with Besiktas.
He was left out of the senior United squad for their tour of the United States by new manager Louis van Gaal and his final appearance for the Red Devils was 45 minutes of action in a pre-season friendly with Southport on Tuesday.
Former United boss Sir Alex Ferguson admitted he had not seen Bebe play in the flesh before signing him.
Good Luck Bebe. This kid was a homeless orphan kid living on the streets, football saved him. And whilst he did not make the grade at United, he has made the grade at the biggest club in Portugal, his home country. He has put his head down and grafted, a model lesson to all. Well done son, and good luck for the future. You deserve the very best.- wotyomamased