The former Belgian prime minister and leader of parliament's liberal group is seeking to replace Martin Schulz, who announced in November he was stepping down to return to German politics.
The outspoken Verhofstadt will be up against Italian Antonio Tajani of the centre-right European People's Party and socialist Gianni Pittella, also from Italy, in the race to run the EU's only elected body.
"In these insecure, turbulent times, when Europe is threatened by nationalists and populists of all kinds we need visionaries, bridge builders and compromise seekers alike," Verhofstadt said in a video on his Facebook page.
"And I want to be one of them," he added.
"It is time for change, time for a broad coalition of all pro-European forces that will put the interests of the European citizens first," he said in the headline.
Verhofstadt was named in September as the European Parliament's lead negotiator on Britain's exit from the European Union, following the British referendum vote to leave on June 23 last year.
But he is expected to give up that position if he wins the presidency of the parliament, with European sources saying it would be too difficult to do both jobs at once.