There had been speculation about the former Fulham manager's future at Sociedad due to the recent election of Badiola, whose new ideas on the club's aims for the season and transfer policy differed greatly to the ones set out following Coleman's arrival last summer.
Having asked for a few days to consider his position, Coleman last Thursday announced he would be staying at Sociedad for "as long as the club need me" after receiving the backing of both his players and Badiola.
However, the 37-year-old Coleman now appears to have had a change of heart and on Wednesday announced to a press conference that he was stepping down as coach.
Coleman joined Sociedad last July on a three-year contract, taking over from Miguel Angel Lotina who was unable to prevent the Basque giants from being relegated from the top flight for the first time in 40 years.
After a slow start to the season which saw Coleman's side win four of their opening 10 league and cup games while also losing five, Sociedad have built up some momentum recently and have now lost just one of their last 11 matches.