In a keynote speech to the SNP conference, the first minister said part-time staff will also receive a “proportionate share” which will be paid by the Scottish government within the current financial year.
Ms Sturgeon insisted there would be “no strings attached” to the payment, but urged Boris Johnson to intervene and ensure the Treasury makes the payment for NHS and social care workers in Scotland tax-free.
Negotiations are currently underway to increase pay for NHS staff, but they "deserve recognition now", Ms Sturgeon said.
"I can announce today that, on behalf of us all, the Scottish Government will give every full-time NHS and adult social care worker £500 as a one-off thank-you payment for their extraordinary service in this toughest of years."
Watch: Stay at home over Christmas is the default message, say Sturgeon
During her speech on Monday to the party faithful, Ms Sturgeon also announced a £100 million fund for people struggling during the winter months, with a £100 cash grant to every family with children in receipt of free school meals to be paid before Christmas.
She said support will also be available to aid homeless people and alleviate the financial pressures of Covid-19 by helping citizens to pay their fuel bills.
"Initiatives like this are not just about providing practical help to those who need it most,” Ms Sturgeon said. "They are an expression of our values and of the kind of country we are seeking to build.
"A more equal Scotland where we look out for each other in a spirit of solidarity and compassion."
Addressing the contentious issue of Scottish independence, Ms Sturgeon also insisted that it is not a “distraction” from the country’s post-Covid reconstructions and argued it was “essential to getting it right”.
She added: “If we want to make sure the country we rebuild is the one we want it to be, with kindness, compassion, fairness, equality and enterprise at its heart, and not one built in the image of Boris Johnson and his band of Brexiteers, we must work to the right plan, with all the tools we need to do the job.”
However, the Scottish Conservative leader Douglas Ross accused the SNP leader of being “totally out of touch with people across Scotland” with the push for a second independence referendum during the Covid-19 pandemic.
He added: “Her plans would devastate the Scottish economy & cost jobs. Indyref2 is the last thing Scotland needs right now.”
In a message to the European Union – just weeks before the Brexit transition period expires – Ms Sturgeon went on: "You are - and always will be - part of who we are. You are not distant to us.
"To those of you who have come from other countries to live here in ours, thank you - please stay. To the other countries of the EU, Scotland wants to return. And we hope to do so soon, as an independent member state."
Watch: Sturgeon says Boris Johnson should not stand in the way of another Scottish independence referendum