UPDATE 1-Australia approves Eldorado buy-out of Sino Gold

* Australia approves Eldorado buy-out of Sino Gold

* Sino Gold listed in Australia but its assets in China (Adds background, valuation)

SYDNEY, Oct 5 (Reuters) - Australia has given foreign-investment approval for Eldorado Gold Corp's (ELD.TO) A$1.58 billion ($1.36 billion) buy-out of Australia-listed Sino Gold Mining Ltd (SGX.AX), Sino Gold said on Monday.

The Canadian firm's offer, announced in August, is worth A$6.73 a share based on Eldorado's last trade, or a 2.7 percent premium to Sino Gold's close last Friday.

The Canadian group already owns 19.8 percent of Sino Gold after buying Gold Fields' (GFIJ.J) stake in the group in July, as it lined up the move to double its gold production in China. (Reporting by Mark Bendeich and Sonali Paul) ($1=1.156 Australian Dollar)