Burgos was a teammate of Simeone's at Atletico and the Argentina national team before linking up with El Cholo again as an assistant at Catania and then Racing Club.
Simeone brought Burgos with him to the Spanish capital in 2011 and he helped secure LaLiga glory for Atletico in the 2013-14 campaign.
Atleti Family, Germán Burgos wants to tell us something. pic.twitter.com/zktDXeXmvz— Atlético de Madrid (@atletienglish) June 3, 2020
The duo have also won a Copa del Rey trophy and two Europa Leagues with Atletico, while on two occasions they were runners-up in the Champions League.
Over recent weeks, it had been speculated Burgos would seek pastures new and he confirmed the news on Wednesday.
"At the end of the current 2019-20 season I will take my first steps as a head coach," he told Atletico's official website.
"I think that with over 10 years' experience in the first division, I'm fully qualified to manage a team.
"It will be influenced by those people who have made me who I am as a coach and a person. I carry them in my soul. Luis Aragones, Carlos Griguol, Marcelo Bielsa… people who have influenced me.
"It's a normal step for a second coach who wants to become a head coach."
On his relationship with Simeone, Burgos added: "He's a friend, we've known each other for such a long time.
"We understand each other with gestures, without gestures, with a glance, with a headbutt. I've said this before but I've had lunch and dinner more times with El Cholo than with my own family.
"We've been together eight years in the Argentina national team, several years at Atletico Madrid as players and eight years here as coaches. It's a lot of time."
Burgos spoke about his favorite moments at Atletico but says he still has ambitions he wants to achieve.
He said: "The celebrations at the Fountain of Neptune, those red and white rivers and there are two specific moments - the first one was when El Cholo and I hugged when we won the league. That first hug, then there's that last hug we had in the changing rooms at Anfield [when Atleti defeated Liverpool in the last 16 of this season's Champions League].
"And – listen to this – we owe ourselves the third one when we win the Champions League, because we have goals to be achieved."