The UEFA President has written to all 209 member associations of FIFA to inform them of his intention to stand, having received indications of support from five continental confederations.
"There are times in life when you have to take your destiny into your own hands," said the Frenchman in the letter.
"I am at one of those decisive moments, at a juncture in my life and in events that are shaping the future of FIFA.
"This was a very personal, carefully considered decision, one in which I weighed up the future of football alongside my own future.
"I was also guided by the esteem, support and encouragement that many of you have shown me."
Swiss incumbent Blatter announced last month he is to step down following the recent crisis which has engulfed FIFA.
He took up the role in June 1998, succeeding Brazil's João Havelange, who was in office for 24 years.
"During this last half-century or so, FIFA has only had two Presidents," said Platini.
"This extreme stability is something of a paradox in a world that has experienced radical upheavals and in a sport that has undergone considerable economic change.
"However, recent events force the supreme governing body of world football to turn over a new leaf and rethink its governance."
Platini has been the President of UEFA since 2007 and a member of the FIFA Executive Committee since 2002.
The former France international has overseen the expansion of the European Championship with next year's tournament set to feature 24 teams, up from the usual 16, and the 2020 edition to be staged across 13 cities in as many countries.
Among those backing Platini is Sheikh Ahmad Al-Fahad Al-Sabah, President of the Association of National Olympic Committees and a member of FIFA's Executive Committee, who is considered a key power broker.
"I am counting on your support and our common love of football so that, together, we can give the tens of millions of football fans the FIFA that they want: a FIFA that is exemplary, united and shows solidarity, a FIFA that is respected, liked and of the people," added Platini.
Polling for the election takes place at an Extraordinary FIFA Congress in Zurich, due to be held on February 26, 2016.
Nominations to stand for FIFA President are due to close on October 26.