The two clubs have been locked in talks over a deal for the Morocco international since the start of the month and the Ligue 1 giants have stood firm on their valuation.
The latest breakthrough means Bouaddi is now on course to complete his prolonged move to England with Lille landing an up front payment of €95M (£81.4m), plus €5M (£4.25M) in performance related add-ons.
Bouaddi is set to sign a five-year contract in Manchester with City retaining the option to extend that by a further 12 months.
City have been on the hunt for midfield reinforcements following Rodri's move to Barcelona - and Tijjani Reinders switch to Saudi Pro League outfit side Al-Qadsiah - alongside a club record £116M deal to bring in Elliot Anderson.
Enzo Maresca is rumoured to still be interested in an offer for his ex-Chelsea playmaker Enzo Fernandez, but time is running out for that transfer to be wrapped up before the summer window closes on September 1st.