Lemar, 22, has become a regular fixture in the France national team squad since making his international debut in 2016.
One of the standout performers for Monaco during their title-winning season and UEFA Champions League semi-final run in the 2016/17 campaign, the technically gifted midfielder will now negotiate personal terms before completing a transfer to the LaLiga outfit.
Capable of featuring at left wing and as an attacking midfielder, Lemar is widely expected to replace Griezmann, who's been linked with moves to FC Barcelona and Manchester United in recent months.
"Atletico de Madrid and AS Monaco has achieved a preliminary agreement over the transfer of Thomas Lemar to our club. Over the next days, both clubs will work to close the agreement for the definitive transfer," read a statement on the club's official website.
Lemar has scored 22 goals and registered 32 assists in 127 games over the past three seasons for Les Monégasques since joining the club from Caen.