"The SFA has concluded a legally binding agreement with Queen's Park FC for the transfer of ownership of... Hampden Park," the SFA said in a statement.
"We have now received notification from Queen's Park that they have accepted the final and binding deal."
The SFA said the transfer of ownership will formally take place on Aug. 1 next year and hoped to ensure it will be a "game-changer" for the association, members and stakeholders.
It added key stakeholders including Scottish Ministers, sportscotland, Big Lottery Fund and Glasgow City Council had been informed of the formal agreement.
"The real work begins now to ensure Hampden Park can continue to serve the needs of the game and be an inspirational home for Scottish football in the future," SFA president Rod Petrie said.
"We can build on the short-term work currently undertaken to make Hampden, Glasgow and Scotland a memorable host city venue for the forthcoming UEFA Euro 2020 finals."
In September 2018, Scotland rejected a potential move to Murrayfield Stadium to continue playing their international fixtures at their spiritual home after 2020.
Hampden has hosted the national team's matches since 1906 as well as major cup finals involving Scottish clubs.
The June 12-July 12 Euro 2020 competition will be played across 12 cities for the first time to mark the 60th anniversary of the competition, with Hampden hosting four games.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Christian Radnedge)
