Earlier in the day, they sacked Abel Resino from the post after a poor start to their campaign.
Atletico are 15th in La Liga with only one win from their first seven games and are rooted to the foot of Champions League Group D without a win or a goal after being hammered 4-0 at Chelsea on Wednesday.
The 44-year-old Sanchez Flores, a former Real Madrid and Valencia defender who was also capped by Spain, is to be presented at the Calderon on Monday morning.
Resino's assistant Santi Denia will be in charge of the team for the visit of Real Mallorca in La Liga on Saturday.
CONSERVATIVE TACTICS
Sanchez Flores guided promoted Getafe to a respectable 13th place in their first ever top-flight campaign in the 2004/05 season before taking the helm at Valencia.
He led his former club to third and fourth place finishes over the next two seasons but was sacked three months into the 2007/08 campaign after a string of poor results.
Last season he steered Benfica to third place in the Portuguese league before stepping down.
His conservative tactics will be important as he is taking over a side with the worst defensive record in La Liga, having conceded 17 goals in seven games.
At an earlier news conference, Resino defended his record after eight months as coach.
"I remain convinced that a couple of good results will change all of this," he said.
The former Atletico goalkeeper had replaced Javier Aguirre in February and engineered a late surge to grab fourth place in the league and a slot in the Champions League playoff round.
Although they saw off Panathinaikos 5-2 to make the group stages in August, the team have struggled since then.
