The 24-year-old, who scored 11 league goals on loan at Pacos de Ferreira last term, failed to cement a regular place at Manchester United following his £7.4 million arrival in 2010Benfica in a deal worth up to €3 million [£2.3m] while Manchester United will also receive 50 per cent of any sell-on fee.
The 24-year-old joined Old Trafford in a £7.4m deal from Vitoria de Guimaraes in 2010, despite Sir Alex Ferguson admitting that he had never seen him play.
Bebe made just seven appearances for United in his debut season and was subsequently loaned out to Besiktas, although a cruciate ligament injury restricted him to featuring in only four games for the Turkish club.
Bem-vindo Bebé | Welcome Bebé | Bienvenido Bebé pic.twitter.com/alk3zYYAeZ— Sport Lisboa Benfica (@SL_Benfica) July 25, 2014
The forward returned to United for their pre-season tour in 2012 but after failing to break into the first team he was sent out on loan to Rio Ave in January 2013.
Bebe was granted another loan move to Portugal at the start of last season and he finished with 11 league goals for Pacos de Ferreira.