Arsenal will pay £45 million plus a further £10m in add-ons for the Brazil international striker with only paperwork and a medical standing in the way of a deal being completed.
The Gunners had already agreed a five-year contract with Jesus.
Arsenal, who have already signed midfielder Fabio Vieira from Porto this summer, are looking to strengthen their squad after missing out on Champions League football.
Jesus, who had only one year remaining on his contract at City, scored 13 goals and gave 12 assists in all competitions for the Premier League champions last season and can play in all attacking positions.
He also excels at pressing and counter-pressing, which are key aspects of Mikel Arteta's playing style.
Meanwhile, Arsenal continue to pursue a deal for Leeds United winger Raphinha and remain confident of adding him to their ranks.