The Frenchman confirmed his departure from Liverpool last month after rejecting a contract proposal, with Madrid offering him an eye-watering package instead.
Konate will earn approximately £400,000 per week and receive a £17.3m signing-on bonus for agreeing to join the Spanish giants, signing a four-year deal at the Santiago Bernabeu.
Arguably one of Europe's best defenders, the 27-year-old is ready to work under new manager Jose Mourinho and become an instrumental figure alongside former Liverpool teammate Trent Alexander-Arnold.
According to journalist Fabrice Hawkins, everything is "finalised" for Konate to join Real Madrid after the World Cup, where France will hope to regain their crown.
France won the prestigious tournament for only the second time in 2018 before losing to Argentina on penalties in 2022, with Konate poised to play a starring role in North America.
The defender will join four other French players at Real, including Kylian Mbappe, Aurelien Tchouameni, Eduardo Camavinga, and Ferland Mendy.