OKDiario is reporting the move is expected to be announced imminently, with the winger set to arrive in Valdebebas at the start of next week.
The agreement was sealed on Sunday after Real Madrid intensified contact with Leipzig in the preceding days. Los Blancos had tracked Diomandé closely throughout the World Cup, where he shone for Ivory Coast, with club scouts present at his side's opening match against Ecuador in the United States.
Sporting director Juni Calafat played a central role in driving the deal forward, while José Mourinho gave the signing his personal backing, viewing the 19-year-old as a source of pace, quality and verticality for his attack.
Diomandé joined RB Leipzig from Leganés last summer after breaking through in Spain's second tier, and continued his development in Germany before his form exploded at the World Cup, where he was named the Bundesliga's best rookie of the season.
Real Madrid had set themselves a hard ceiling of €100 million plus a maximum of €30 million in add-ons, regarding anything beyond that as excessive given the player's age and inexperience at the top level — but held firm and got the deal done within those parameters regardless.
The transfer represents a significant coup given the level of competition involved. PSG had appeared to have the move all but arranged before Real Madrid entered the race and changed the picture entirely, while Liverpool also made a push, having an £85 million bid rejected earlier in the process. Leipzig, who paid Leganés around €20 million for Diomandé only 12 months ago, stand to make a substantial profit on a player who has become one of the most sought-after young attackers in world football within a single season.
The signing continues Mourinho's rapid reshaping of the Real Madrid squad since his return to the club, following the earlier arrivals of Bernardo Silva, Marc Cucurella, Denzel Dumfries and Ibrahima Konaté this summer.
Diomandé is expected to sign a long-term contract through to 2031, giving Real Madrid control of one of the game's most in-form young wingers for the majority of the next decade. His arrival also has knock-on implications elsewhere in the squad, with the club's forward line now so heavily stocked that a departure elsewhere in attack, potentially involving Vinícius Júnior, is considered increasingly likely before the transfer window closes.