The BBC has learned that Platini - after receiving indications of support from four continental confederations - will be a candidate when polling takes place on 26 February.
The 60-year-old former France and Juventus midfielder could declare as early as Wednesday.
Switzerland's Sepp Blatter, 79, has been in charge of Fifa since 1998.
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He is standing down as a result of a corruption crisis at world football's governing body.
Platini is the overwhelming favourite to replace him.
As well as the backing of his own European confederation, he is understood to have gained support from:
If every football association within those confederations voted for Platini, he would secure 144 votes, which is more than enough for him to be elected as Blatter's successor.
That is unlikely to happen, however, given some football associations will back rival candidates or abstain.
Nevertheless, Platini is still expected to poll a significant number of votes.
The election will be held in Zurich at an emergency congress attended by the Fifa member associations.
Candidates have until 26 October to be nominated.
As a player, Platini won three Ballon d'Or titles in the mid 1980s as well as a European Cup, Cup Winners' Cup and Super Cup with Juventus.
The former Nancy and Saint-Etienne midfielder, who became famous for his ability to score from free-kicks, also won league titles in France and Italy.
He also helped France to European Championship success in 1984 and third place at the 1986 World Cup.
Platini was elected Uefa president for a third term in March, when he stood unopposed.
He marked his re-election by:
Under his presidency, Uefa has seen a number of major developments.
Next year's European Championship will feature more teams than ever, up from 16 to 24. Then in 2020, the tournament will be staged in 13 cities across as many countries.
In club football, the Champions League has grown in popularity, with British broadcaster BT Sport agreeing to pay £900m for exclusive live rights to European football's top club competition from 2015-16.
However, Platini has faced criticism, largely over his support for Qatar's staging of the Fifa World Cup in 2022.
Uefa president Michel Platini will announce later this week he wants to be the next president of Fifa.