Van Praag, announcing his bid on the Dutch FA's website, said UEFA had drifted into an impasse since Platini was suspended and he warned it faced the threat of a breakaway league being formed from Europe's top clubs.
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The 68-year-old said he wanted to use "my experience, knowledge and networks to make UEFA a cohesive unit again."
He said the challenges facing UEFA included "the threat of clubs who want to start their own league, the structure of the club competitions, human rights, discrimination and the tremendous changes in commercial marketing in football."
UEFA's acting secretary general Theodore Theodoridis said the election would take place in Athens on September 14 - meaning that UEFA will not have a president during its showpiece European championship in France in June and July.
Theodoridis said senior vice-president Angel Maria Villar would be responsible for presenting trophies in the meantime, starting with Wednesday's Europa League final between Liverpool and Sevilla.
Platini, a former French international regarded as one of the finest players of his generation, was one of the sport's most powerful figures until he was engulfed by scandal.
The 60-year-old was banned, along with former FIFA president Sepp Blatter, over payment of two million Swiss francs (£1.4 million) made to the Frenchman by FIFA with Blatter's approval in 2011 for work done a decade earlier.
FIFA's ethics committee said the payment, made at a time when Blatter was seeking re-election, lacked transparency and presented conflicts of interest. Both men denied wrongdoing.
He was initially suspended for eight years, later cut to four years on appeal by the Court of Arbitration for Sport (CAS).
UEFA said they were still waiting for a reply from FIFA on exactly what Platini could and could not do following his ban, especially with regards to Euro 2016 in the Frenchman's homeland.
"There is a grey zone and that grey zone needs to be clarified with FIFA," UEFA's legal director Alasdair Bell said."It's only fair and reasonable for him to be told what the sanction means."
(Reporting by Brian Homewood; Editing by Richard Balmforth)
