Casillas is still contracted to FC Porto, where he has played since leaving Los Blanco in 2015.
Casillas suffered a heart attack in May last year and is yet to return to the field, though he has not formally retired from the game.
The 38-year-old will contest Luis Rubiales for the position, with elections set to be held later in the year.
He wrote on Twitter: "Yes, I will stand for the presidency of the RFEF when the elections are called. Together we will put our federation at the height of the best football in the world: that of Spain.
"I have informed the president of my club, FC Porto, of this decision, to whom I can only express my deepest gratitude.
"We are working with the utmost respect in our candidacy. More than 23,000 voters await us in fair and transparent elections. 139 assembly members will decide.
"Thank you all for all the love I have continually received. Your support and your strength encourage me. Let's go for it! #IkerCasillas2020"
Casillas,38, is widely considered as one of the greatest goalkeepers of his generation.
In 16 years at Real Madrid between 1999 and 2015, Casillas won three UEFA Champions League trophies, five Spanish La Liga titles and two Copa del Reys, amongst numerous other trophies.
Casillas, who holds the record for most appearances in the history of the UEFA Champions League (177), captained Spain to win the European Championships in 2008 and 2012 as well as the FIFA World Cup in 2010.
