The midfielder, who only has one year left on his contract with the Ligue 1 club, will undergo his medical on Tuesday in Clairefontaine, where is he training with France's under-21 squad.
Camavinga's transfer is expected to be made official on Tuesday. Rennes didn't want to see the player leave as a free agent next summer and are said to be satisfied with the deal.
The deal with Rennes was agreed late on Monday night after the discussions with Paris Saint-Germain over the transfer of Kylian Mbappe stalled. However, sources close to the Bernabeu insisted that the deal was not connected to the breakdown in talks to sign Mbappe.
Madrid have been following Camavinga for several seasons, with former manager Zinedine Zidane a longtime admirer of the player who made his Ligue 1 debut as a 16-year-old. There's a belief at the club that he's the right age to learn from -- and eventually take over from -- Toni Kroos and Luka Modric at the heart of Madrid's midfield.
Camavinga, who was called up for France U21 by Sylvain Ripoll for the Euro 2023 qualifiers in September, also has three senior appearance for Les Bleus.
While Camavinga is not the French superstar that Real Madrid and their fans expected this summer, he was a very coveted player. PSG, Liverpool, Chelsea, Manchester United, Borussia Dortmund were all interested in him. He is a complete midfielder, excellent on the ball with great activity and energy.
ESPN Madrid correspondent Alex Kirkland contributed to this report.