Virgin Australia chief executive John Borghetti said the transactions were part of his airline's strategy to become the airline of choice in all markets.
"Singapore Airlines had been an important strategic alliance partner of Virgin Australia, and we are very pleased to have their support as an investor," he said.
"We believe this investment demonstrates their confidence in our strategy and it enables Virgin Australia to fast-track its growth plans."
Air New Zealand last year built up a 19.9 per cent stake in Virgin Australia to give it a slice of the domestic market across the Tasman and allow better connectivity and capacity management across the Tasman.
Middle Eastern airline Etihad has also taken a 10 per cent stake in Virgin Australia, whose shares have rallied by more than 60 per cent this year.
The moves are part of growing equity alliances among airlines as they battle more competition and high fuel costs.
Last month struggling Qantas announced a global partnership with Emirates to improve its links to Europe and allow it to cut loss-making, long-haul routes and focus on its profitable domestic flights and budget airline Jetstar.
Borghetti said the Tiger deal allowed Virgin Australia to access the budget market and enabled Tiger Australia to grow, "providing greater competition to this important market segment".
The domestic plans require regulatory approval.
Craigs Investment Partners analyst Chris Byrne said Singapore's buy-in to Virgin reflected the growing move by airlines to create stronger ties rather than looser arrangements such as code shares.
"Everyone is looking to consolidate those relationships, and equity investments bed these down. Air New Zealand has shown the way - they've done very well out of their relationship with Virgin."
The deals
*Singapore Airlines buys 10 per cent in Virgin Australia.
*Virgin buys 60 per cent of the existing shares in Tiger Australia.
*Virgin will buy all of regional carrier Skywest.