The 28-year-old will now discuss personal terms and have a medical at the Premier League club.
Luis looks likely to be a direct replacement for ex-England left-back Ashley Cole, who joined Roma last week.
“It has been a few memorable years. Thank you for supporting me always Atletico,” Luis tweeted on Wednesday.
Atletico said the ex-Deportivo La Coruna player told them he wanted to join Chelsea at the end of the season.
He will become the second Atletico player to sign for Chelsea this summer, with Spain striker Diego Costa having already completed a £32m move .
Luis has played 180 matches for Los Rojiblancos since arriving from La Liga rivals Deportivo in the summer of 2010.
He has won four caps for Brazil, who named him on their standby list for their 2014 Fifa World Cup squad.[BBC]