England suffered a 3-2 penalty shoot-out loss on home soil to Italy on 12 July after a 1-1 draw after extra time in its first major tournament final in 55 years.
The showpiece match was overshadowed by a security breach that saw a number of ticketless supporters enter the stadium and clash with fellow fans and stewards.
UEFA last week launched its own investigation and hit the FA with four charges relating to fan disorder, including the throwing of objects and the lighting of fireworks.
The unsavoury scenes prompted Julian Knight MP, the chair of the Digital, Culture, Media and Sport Committee (DCMS), to write to FA CEO Mark Bullingham demanding answers.
And in a statement released on Monday, the FA has vowed to identify those responsible for the trouble before, during and after the game.
"We are determined to fully understand what happened outside and then inside Wembley Stadium at the Euro 2020 final on July 11," the statement read.
"We informed DCMS 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."
The FA was also previously fined €30,000 (£25,630) by UEFA for the behaviour of supporters during the semi-final win against Denmark, which included a laser being shone at Denmark goalkeeper Kasper Schmeichel.