Italy went on to beat England on penalties to lift the trophy but prior to kickoff, a group of supporters without tickets breached the Wembley Stadium security and entered the ground.
Police said they had arrested 49 people while policing the final following the match and added that 19 officers were injured in clashes with volatile crowds around the stadium.
The FA released a statement on Monday which read: "We are determined to fully understand what happened outside and then inside Wembley Stadium at the UEFA EURO 2020 Final on Sunday 11 July 2021.
"We informed DCMS [Department for Digital, Culture, Media and Sport] at the weekend that an independent review led by Baroness Casey of Blackstock has been commissioned to report on the facts and circumstances involved. It will speak to all parties concerned and include external experts.
"A key emphasis of the findings will be to ensure that lessons are learned and such disgraceful scenes are never able to be repeated.
"We continue to work with the relevant authorities in support of their efforts to identify those responsible and hold them to account."
After the match, England and Manchester United defender Harry Maguire revealed his father was left with rib injuries and struggled to breathe after being trampled by supporters during crowd disturbances.
UEFA has also opened a formal investigation into the storming of Wembley, in addition to charging the FA with four separate offences relating to the conduct of fans.