The former Western Province centre was diagnosed with Motor Neuron Disease (MND) last year and died, aged 45, on Monday.
Linee played 112 matches at centre for his province between 1992 and 2001. He made his Springbok debut in 1993, aged 23.
He played nine tour matches for his country in Australia, Wales, Scotland, and Ireland between 1993 and 1994, but was never capped in a Test.
His funeral service will take place at the Huguenot Church, Paarl, on Saturday at 10am.