Verhofstadt will keep the Conference of Presidents (comprising the EP president and group leaders) fully informed of developments and will help prepare the EP position in the negotiations, in close consultation with the Conference of Presidents.
The former Belgian Prime Minister said in a tweet that he was honoured by the appointment:
Verhofstadt's appointment may cause concern for some who disagree with his federalist views. He campaigned for Britain to remain in the EU and has previously aired his opinion that it would be "wrong" to take Scotland out of the bloc despite the result of the referendum.
Indeed, former Ukip leader Nigel Farage said Verhofstadt's appointment should mean Brexit negotiations are shorter.
"Guy Verhofstadt hates everything we stand for which should mean a much shorter renegotiation," he commented.
Mr Verhofstadt is a fanatical supporter of EU federalism even by the standards of the European Parliament. This appointment will no doubt speed up the UK's exit from the European Union.
The announcement comes after European Council president Donald Tusk told Theresa May to start the Brexit negotiations process as soon as possible at a meeting this morning.
Verhofstadt said in June that he could not understand why Brexiteers did not want to trigger Article 50 as soon as possible, and last month said he agreed with French President Francois Hollande that Brexit should be completed by 2019.
"While I campaigned for Britain to remain in the European Union, a clear majority of voters in the UK made the decision to leave," he said in August.
"This choice must now be respected. It is only fair that negotiations take place as soon as possible and conclude before the next European elections, due in 2019.
"If negotiations are dragged out beyond this timeframe, then Brexit could become an even greater distraction from the real challenges the European Union is facing."