The 28-year-old Brazilian will complete a move to Jose Mourinho's team as long as personal terms can be agreed.
Luis will give Mourinho the extra option he needs at left-back following the departure of the experienced Ashley Cole, who was allowed to leave when his contract expired at the end of last season and has signed a deal with Roma.
Cesar Azpilicueta ws preferred to Cole at left-back for much of last season but is a right-back by trade and Luis's arrival may allow him to switch back to his favoured side.
Luis was a key player for Atletico during their incredible 2013/14 campaign, when they won the La Liga title for the first time since 1996 and lost to local rivals Real in the Champions League final.
The former Deportivo man made 44 appearances over the course of the campaign and many experts felt he should have been selected for the Brazil World Cup squad but he was only named as a stand-by.
His potential move to London has been in the works for a while and Sky Sports understands the transfer fee agreed is for less than the £20m which has been widely reported.
An Atletico statement read: "Atletico Madrid and Chelsea have reached an agreement to transfer the rights of Filipe Luis, pending a medical with the English club.
"The Brazilian player told our club at the end of the campaign about his willingness to join the London side.”
Chelsea already have one former Atletico player in their ranks for the upcoming season after forward Diego Costa signed a five-year deal on Tuesday.