The transfer is understood to be worth £60 million upfront, with another £5 million available through performance-related add-ons.
Tottenham had also reached an agreement with Everton for the 26-year-old on Friday night, with the proposed deal linked to the possibility of Richarlison returning to his former club.
However, the move broke down after Richarlison failed to agree personal terms with Everton.
The Merseyside club had reportedly offered around £35 million for the Brazilian forward.
With Richarlison’s transfer unable to move forward, Tottenham could not complete their proposed deal for Iliman Ndiaye.
Richarlison later addressed the situation in an emotional post on Instagram, making it clear that he wanted control over his own future.
The Brazil international said he would be open to returning to Everton if an agreement was reached between the two clubs, but insisted that he would not allow others to determine his next move.
He also confirmed that he remains under contract at Tottenham and is ready to continue with the club.
Tottenham have since turned their attention to Chelsea winger Mykhailo Mudryk, with discussions taking place over a possible season-long loan.
For Manchester City, the agreement to sign Ndiaye comes after their attempt to bring in Liverpool forward Cody Gakpo appeared to fall through.
City had been negotiating with Liverpool over an £80 million deal for the Netherlands international.
Liverpool were prepared to consider selling Gakpo, but only if they could bring in another attacking player first.
The Reds completed the signing of France winger Bradley Barcola from Paris Saint-Germain on Monday in a deal that could reach £123 million.
However, they still wanted to add another forward before allowing Gakpo to leave.
Liverpool had explored deals for Brighton winger Yankuba Minteh and Crystal Palace forward Ismaila Sarr, but the clubs’ valuations have made both transfers difficult.
Gakpo, 27, is now expected to remain at Liverpool unless the club can complete a deal for another winger before Tuesday’s transfer deadline.
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