The news was given to MEPs by outgoing President Martin Schulz at the start of the plenary in Strasbourg.
Verhofstadt was one of six candidates to succeed Schulz, who is returning to German domestic politics.
No reason was given and each of the remaining candidates gave a three minute presentation to the Parliament.
The new overwhelming favourite, EPP group candidate Antonio Tajani spoke in three languages - Italian, French and English.
He said, "I believe in Europe, but we need to change. We need a strong Parliament, a President, not a Prime Minister. One who has experience, and I put my years of experience at your disposal.
"We need a more democratic Europe and not close ourselves off in our Ivory Tower in Europe. I don't have a manifesto but, on Brexit, we will need to be balanced and defend the EU, but the UK will be an important partner of ours."
One of three Italian candidates and a former European Commissioner, he said, "I would remind you that I refused my golden handshake from the Commission because it felt unfair to take €500,000 at a time of great austerity. That a Commissioner should get such a sizeable amount of money seemed unfair.
"If elected, I will reduce the number of people in the President's cabinet, promote gender balance and have a member dedicated to furthest regions."
He concluded by saying, "I don't share everything Voltaire said but this Parliament and EU is the cradle of democracy and we need to defend it."
The Socialist candidate, Gianni Pittella, told a packed chamber, "I am standing because I want a braver Europe, one able to face the challenges we face in the world. This Parliament needs to be where everyone can debate.
"But, whatever happens today, we will never again have a grand coalition in this House… a privileged agreement between the main groups," said the Italian, who has seen his chances seriously diminished by a last minute deal brokered between the EPP and ALDE groups.
"If elected, I will guarantee this exchange of ideas and that Parliament is as inclusive as possible. I will do all I can to ensure the Parliament is utterly transparent. This will be a Parliament which is able to be present in places where people are suffering.
"I have come a long way, from a village in southern Italy, but that feels very distant from here these days. From the bottom of my heart, if elected I will push your hopes and dreams."
Jean Lambert, the candidate for the Greens group, said, "It is clear Parliament needs to change and the end of the grand collation is an opportunity to elect someone other than one of the usual suspects and dare to elect a woman and, if it is really feeling radical, someone from the UK, though I know that is difficult for some here."
She added, "We're in shifting political times and I would be honoured to President."
Eleonora Forenza, of the GUE/NGL group, said, "I want to represent hope not a political group. I am a feminist and that can make a difference from the jackets and ties who have taken the Parliament in the past.
"We're being asked which candidate we will support in the later rounds of this election but I ask whether that candidate should come from within the grand coalition. My message is that I aim to bring hope to a new generation."
Belgian MEP Helga Stevens, from the ECR group, said, "Standing here today reminds me of the first time I entered this Parliament as an MEP and the excitement I felt. But all that I have seen in the years since is an old boys' club, middle-aged men seeking to dominate. That is not fair or open. My purpose is to ensure every voice here matters.
"My message is: Vote for the candidate who wants to stand up for all 750 of you and shows Europe we are here to represent every single citizen and who will listen. Now I might be deaf but I am a very good listener. Let us make a bold and decisive step to change and breathe some fresh air into this building. No more old boys' club or back room dealing."