The council launched the fund to help those affected by the weekend tragedy with a contribution from its existing charitable funds.
And Mr Salmond has now said the Scottish Government will match the donation.
The appeal has been set up to support people facing hardship as a result of Friday's disaster, including casualties and the families of the nine people who lost their lives.
Within minutes of the appeal launch offers of cash came flooding in.
Lord Provost Sadie Docherty has already received a number of generous offers of support.
She said: "Around the world, people have admired the courage shown by ordinary Glaswegians whose first instinct when tragedy struck was to run towards danger to help those in peril.
"Today, that desire to help is still strong and the Clutha Appeal Fund will give the city an opportunity to make sure the care, compassion and solidarity the city has shown in the last few days continues.
"Glasgow is famous for its heart and its generosity and I am very proud, but not at all surprised so many people across the city want to help those who are suffering."
Mr Salmond announced the Government's cash donation during a statement to the Scottish Parliament.
He said: "Glasgow City Council has established a fund for affected families and I can confirm the Scottish Government will match the council's contribution."
Anyone in need of emotional or practical support can call a dedicated helpline on 0141 287 0999.
Businesses, charities or individuals wishing to donate by debit or credit card should call 0141 287 7878.
Donations can also be made by cash or cheque at the council's Service Desk at 45 John Street, Glasgow, G1 1JE.
Bank payments can be made to Clutha Appeal Fund, Sort Code: 83-44-00, Account 10804129.