The Australian's removal from the position, confirmed in a statement as a decision to "step down", was reported three weeks ago.
It followed Scotland's failure in November to qualify for the T20 World Cup when they were unable to finish in the top six of a 16-team tournament.
Steindl said: "The decision to step down has been a difficult one but I feel it is the right one for the team's immediate future. I have enjoyed the challenges that the job has involved and feel privileged to have worked in this role for the last six years.
"I have been lucky enough to work with some very good cricketers in this time and I take particular pride in overseeing and helping establish Scotland's first professional structure. I hope this system will be built upon and improved in years to come."
Steindl, who led Scotland to the T20 World Cup in 2009 as well as the Intercontinental Cup final in 2010, added: "I will always treasure the special memories of singing 'Flower of Scotland' after every win with my team-mates. I wish the team every success in the future."
Roddy Smith, chief executive of Cricket Scotland, praised Steindl's contribution to the Scotland side, stating: "Peter took on the national team at a transitional time and has worked tirelessly to improve the team individually and collectively. His decision to step down from the role at this time, in his belief that this is in the best interest of the team, shows his commitment to the squad and his desire that they succeed.
"I would like to publically thank him for his effort, commitment and professionalism during his time as head coach of the Scotland team."
Steindl now plans to spend time with his family while the team, led by interim joint coaches Craig Wright and Paul Collingwood, take part in the 50-over World Cup qualifiers in New Zealand.