The meeting in Brussels, chaired by the assembly’s Brexit coordinator Guy Verhofstadt, comes just ahead of the expected official EU reaction to Johnson’s election later on Wednesday.
Other Brexit steering group members expected to attend include Elmar Brok and Danuta Hubner.
With the outgoing European Council President Donald Tusk still to comment, the new President of the European Commission, Ursula von der Leyen, has already cautioned that there were “challenging times ahead” and that both sides had a “duty” to deliver a deal on Brexit.
The UK is due to leave the EU on 31 October.
Von der Leyen said, “It is important to build up a strong working relationship because we have a duty to deliver something which is good for the people in Europe and the United Kingdom.”
Barnier, the EU’s chief Brexit negotiator, also responded to the elevation of Johnson by calling for them to work “constructively” for “the ratification of the Withdrawal Agreement.”
In a vote of Tory party members, Johnson swept to a convincing victory over UK foreign minister Jeremy Hunt – winning two-thirds of ballots cast by the 87.4 percent of those who voted.
"A new YouGov poll has revealed that 34 percent of the British public believe Johnson would make the best Prime Minister, with 20 percent choosing Labour leader Jeremy Corbyn, and 42 percent saying they do not know"
Johnson will deliver his first speech as Prime Minister later on Wednesday afternoon outside Downing Street and is then expected to appoint his new Cabinet of ministers in the evening.
As he prepares for his first full day as Prime Minister, a new YouGov poll has revealed that 34 percent of the British public believe Johnson would make the best Prime Minister, with 20 percent choosing Labour leader Jeremy Corbyn, and 42 percent saying they do not know.
On Tuesday, Corbyn said that his party would put forward a motion of no confidence in Johnson’s Government but that this would be “at a time of our choosing.”
There are reports that Labour would trigger a no confidence vote after the UK Parliament’s summer recess, which begins on Thursday.
In the wake of Johnson’s widely-expected victory over Hunt, at least three Cabinet ministers - Chancellor Philip Hammond, Justice Secretary David Gauke and International Development Secretary Rory Stewart - are expected to resign on Wednesday before Johnson officially takes over from Theresa May.
Hammond previously announced at the weekend that he would resign on Wednesday and, while Gauke and Stewart congratulated Johnson, a former London mayor and UK foreign minister, on his victory, both said they would be returning to the backbenches.
Government Whip Mark Spencer, meanwhile, has been appointed Chief Whip, while former International Development Secretary Priti Patel and Employment Minister Alok Sharma will reportedly join Johnson’s new Cabinet.
There are reports that Johnson’s former special adviser David Frost will be his Europe secretary.