The sale will be conducted through a share placing at a discount to the market price, which is expected to raise around $890 million.
Britain's biggest drugmaker said on Thursday it would remain a 6.2 percent shareholder in Aspen and it had undertaken not to sell any more shares in the South African group for 180 days.
A source familiar with the matter said a price range of 365 to 385 rand per share had been set for the placement, representing a discount of 5.3 to 10.2 percent to Aspen's closing price on Thursday.
The share sale is being run by Citi (C.N) and UBS UBSN.S.
Simon Dingemans, GSK’s chief financial officer, said the disposal would help give his company flexibility to invest in new opportunities in the wake of a $20 billion-plus asset swap transaction with Novartis NOVN.VX.
"As we continue to reshape the group around our core franchises and drive the benefits from the Novartis transaction, optimizing our financial flexibility to invest behind these priorities is key," he said in a statement.
"As a result we have decided now is the right time to realize further value from this successful relationship. We continue to believe in the strategy of Aspen and we remain committed to working together in the future.”
GSK said that the net profit on the disposal would not be included in core operating profit and core earnings in 2015, and GSK would no longer account for Aspen as an associate.
Reporting by Freya Berry, Vikram Subhedar and Ben Hirschler; Editing by Pamela Barbaglia, Greg Mahlich