Ivanov, twice Bulgarian Footballer of the Year, was officially presented to the media at a news conference on Wednesday, replacing Emil Velev, who was fired following Lokomotiv's disappointing start to the season.
Ivanov, 36, who resigned as Levski Sofia coach in April, decided to quit after a training session on Thursday, saying he despaired of the "organisational chaos". The club's owner Veselin Mareshki failed to persuade him to return at an emergency meeting on Friday.
Lokomotiv's administrative director Atanas Uzunov also resigned, saying he did not want to face fans who criticised him for the club's policies, and honorary president Hristo Bonev announced he would "no longer occupy any position at the club".
Lokomotiv, champions in 2004, have won one of their eight league games so far this season and are 13th in the table with eight points.
Last month, players and coaches at Lokomotiv passed lie-detector tests after Mareshki said he wanted to make sure there were no suspicious factors behind their 1-0 loss to lowly Botev Vratsa. The tests were criticised by the world players' union FIFPro.
Mareshki would announce the new coach live on state television on Saturday, the club said.