PSG had reached a preliminary agreement with Diomande's representatives around three weeks ago and appeared close to finalising a fee with RB Leipzig, but Real Madrid entered the race late and moved to increase their offer to both the player and the club, with the transfer now expected to exceed €100 million.
PSG confirmed their withdrawal in a strongly worded statement on Sunday night.
"Paris Saint-Germain has officially withdrawn its interest this evening and has ended all negotiations relating to Yan Diomande.
"The amount requested for the transfer, as well as the salary demands, were completely disproportionate and could destabilise the market.
"PSG will not abandon its principles of rigorous financial management and squad balance," the club said, adding a pointed remark aimed at the player's representatives: "Paris Saint-Germain, back-to-back European champions and the most decorated club in recent years, will not be dragged into inflationary games or the manoeuvring of certain intermediaries.
"The club will continue, calmly and with confidence, its strategy in the transfer market."
Diomande will fly to Madrid in the coming days to complete a medical and sign a contract running until 2031. The Ivory Coast international joined RB Leipzig from Leganés for around €20 million last summer and went on to score 15 goals and provide 11 assists in 46 appearances across all competitions, catching the eye further with a series of strong performances for his country at this summer's World Cup.
The move represents Real Madrid's fifth signing of the summer, following the arrivals of Ibrahima Konaté, Marc Cucurella, Denzel Dumfries and Bernardo Silva, and continues a pattern of reinforcing multiple positions in defence and now attack as José Mourinho reshapes the squad for his first full season back in charge.
Real Madrid's late entry into the race caught PSG by surprise, with the French champions reportedly still confident of winning the race for Diomande as recently as Sunday morning despite being aware of Real Madrid's interest.
The scale of the increased offer, to both Leipzig and the player personally, ultimately proved decisive. Manchester City and Liverpool had also been credited with interest in Diomande earlier in the process, but neither club advanced talks as far as PSG or Real Madrid before the winger's future was resolved in Madrid's favour.