A statement on Atletico’s website confirmed the clubs will work over the next few days to complete the transfer.
The 22-year-old is currently at the World Cup with France, who are due to play their first game of the tournament on Saturday against Australia.
Lemar, who joined Monaco in 2015, has made 12 appearances for his country since making his debut against the Ivory Coast in November 2016.
The winger became an integral part of Monaco’s team during his three-year spell, and starred in their shock Ligue 1 triumph in 2016-17, a season where they also reached the Champions League final.
Monaco’s exploits saw Bernardo Silva, Benjamin Mendy and Tiemoué Bakayoko among those to move on last summer, while Kylian Mbappe moved to PSG on loan with a view to a permanent move.
Lemar was linked with moves to Arsenal and Liverpool 12 months ago, but it appears he will now swap the Ligue 1 for La Liga after Monaco reached an agreement with Atletico.