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The move comes after fans taunted England's black players with Nazi salutes and monkey chants during a Euro 2020 qualifier in Sofia, prompting match officials to halt the game twice.
Prime Minister Boyko Borissov had called earlier for Mihaylov, a former goalkeeper and Bulgaria international, to go.
The fallout from what English FA chairman Greg Clarke described as "probably one of the most appalling nights I have seen in football" also triggered calls for urgent action from anti-racism campaigners and politicians.
A spokesman for British Prime Minister Boris Johnson said European governing body UEFA - the tournament organisers - needed to do more to tackle "vile" racism.
The issue has long been a blight on European football, with racist incidents during matches reported sporadically and abuse levelled at players on social media.
UEFA, the administrative body for the sport in Europe, had already ordered the partial closure of Sofia's Vasil Levski stadium for the England game after racist behaviour by Bulgarian supporters in June's qualifiers against Czech Republic and Kosovo.
UEFA president Aleksander Ceferin said that football could not solve the problem on its own, and politicians must play a greater role.
"Football associations themselves cannot solve this problem. Governments too need to do more in this area. Only by working together in the name of decency and honour will we make progress," the Slovenian said in a statement.
FIFA, the global governing body for soccer, threatened to extend punishments levelled against sides globally in light of events at the match in the Bulgarian capital.
"FIFA may extend worldwide any sanctions that a Confederation or Member Association imposes for racist incidents, such as those which occurred in Sofia during the UEFA EURO 2020 qualifier match between Bulgaria and England," the Zurich-based organisation said.
MATCH HALTED TWICE
Yesterday's match was temporarily halted by the Croatian referee under a three-step UEFA protocol, but the stoppage did not go far enough for some anti-racism activists who felt the England players should have walked off.
Anti-racism organisation Kick It Out said UEFA's existing sanctions were not fit for purpose and called for Bulgaria to be booted out.
"There can be no more pitiful fines or short stadium bans. If UEFA care at all about tackling discrimination - and if the Equal Game campaign means anything - then points deductions and tournament expulsion must follow," it said.
UEFA said it had opened disciplinary proceedings against Bulgaria on a number of charges including racist behaviour and the throwing of objects.
England were also charged for disruption of the national anthem and an insufficient number of travelling stewards.
Mihaylov had previously defended Bulgarian football from accusations of racism and criticised England for what he saw as a "fixation" on potential incidents that could raise tension.
His departure came just hours after a Bulgarian Football Union (BFU) spokesman said Mihaylov would not resign because the state had no right to interfere in football.
A later statement said that Mihaylov's formal resignation would be presented to the Executive Committee on Friday.
"His position is a consequence of recent tensions; an environment that is detrimental to Bulgarian football and the Bulgarian Football Union," it said.
Reuters was not able to reach Mihaylov by telephone on Tuesday.
More than 20 police officers swept into the (BFU) headquarters on Tuesday afternoon.
But the Bulgarian chief prosecutor's spokeswoman said that the operation was part of an investigation conducted by the Specialized Prosecutor's Office, and so not directly related to the racism row.
"It's about crimes against sport," Rumyana Arnaudova told Reuters. "We're talking about corruption offences, connected to the work of the BFU's referee commission and the appointment of referees on football matches.
"The investigation is still under way and it's too early to say if there'll be some arrests."
Mihaylov, captain of the Bulgarian national team that made it to the World Cup semifinals in 1994, has been heavily criticised by local media and football fans for failing to lead the BFU out of years of corruption and controversy.
Bulgaria have failed to qualify for a major tournament since 2004, while Mihaylov's tenure has been marred by allegations of cronyism. He has denied such allegations in the past.
There have been widespread reports of match-fixing in Bulgaria in recent years but little in the way of progress in holding anyone accountable.