The Scottish Government has given approval for 12,000 spectators to be in the stadium – 25% of the stadium’s capacity.
A final decision from Uefa on the plan is expected to come on Friday.
Earlier, Ms Sturgeon suggested there would be a “reasonably good number” of fans in the stadium
Scotland are due to play the Czech Republic on June 14 and Croatia eight days later.
The First Minister said: “I’m delighted we have been able to confirm that, thanks to Scotland’s progress in suppressing Covid-19, 12,000 spectators will be able to attend Hampden for the four Euro 2020 games this summer.
“This is a significant moment which celebrates just how far Scotland has come in tackling the Covid pandemic.
“Allowing fans to come together to watch Scotland play at our national stadium is a huge milestone, thanks to the dedication of fans sticking to the public health guidance.
“The restrictions set out over the last year have been really difficult for everyone – but I am looking forward to joining the Tartan Army in cheering on Scotland in June at Hampden Park.
“The country has delivered for the fans – now it’s all eyes on the team to deliver the results!”
UEFA is expected to contact all ticket holders by the end of this week advising them on the latest tournament arrangements including ticketing and travel information.