Councillor Brookfield, who was 57, died after a fearless battle with cancer.
A physical book of condolence is available at the Civic Centre, St Peters Square, Wolverhampton WV1 1SH for people to leave their tributes. The Civic Centre is open Monday to Thursday 9am to 5pm and Friday from 9am to 4.30pm.
Meanwhile, people can leave tributes via an online book of condolence to remember Councillor Brookfield.
Both books of condolence opened today, with the Mayor of Wolverhampton Councillor Dr Michael Hardacre, among those leaving tributes at the Civic Centre this morning.
Mayor Councillor Hardacre said: "I was very saddened to hear of the death of Councillor Brookfield.
"He was a proud and committed leader of our city, dedicated to the citizens of Wolverhampton, and the heartfelt tributes we have seen from people across the political spectrum is testament to this.
"As we mourn, we have opened books of condolence at the Civic Centre and online so that residents can pay their own respects to Councillor Brookfield."
Also signing the book of condolence this morning were Deputy Leader of the Council Councillor Stephen Simkins, Conservative Councillor for Tettenhall Regis Udey Singh and the Chief Executive of the Council, Tim Johnson.
The City Flag and the Union Flag will be flying at half mast outside the Civic Centre until Councillor Brookfield’s funeral, details of which will be announced in due course.
