SIA currently owns 55.8 per cent of Tigerair and the "voluntary conditional general offer" is for the shares it does not already own valued at around 453 million Singapore dollars (USD 322 million).
The airline said it intends to delist the budget carrier from the stock market.
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"SIA's objective for the offer is to derive enhanced commercial and operational synergies through a full integration of Tiger Airways into the SIA Group," the airline said in a statement.
"SIA believes the Offer will benefit shareholders of both Tiger Airways and SIA."
The airline is offering Tiger shareholders a price of 0.41 Singapore dollars per share in cash and an option to subscribe for SIA shares at 11.1043 Singapore dollars.
SIA shares closed at 11.15 Singapore dollars apiece yesterday before the carrier announced that its second quarter net profit more than doubled.
Tiger shares closed at 0.31 Singapore dollars yesterday, meaning SIA's offer price carries a 32 per cent premium over that.
SIA said its offer will be funded from its "internal cash resources".
The airline said its net profit in the three months to September soared 135 per cent to 213.6 Singapore dollars million from the previous year, boosted by higher dividends from long-term investments and the absence of share loss from associated companies after it classified Tiger as a subsidiary.