The Riverside Stadium outfit - who were pre-season favourites to lift the Championship title and return to the top flight - are languishing in 20th place following the first 11 games of the campaign.
Strachan leaves after 46 games in charge, winning just 13 of them.
"Gordon is a man of great integrity. He has torn up his contract and walked away without compensation because he felt it was in the best interests of this football club," chairman Steve Gibson told the club's official website.
"There are very few managers who have ever done that but that is the mark of the man. He feels he has given it everything he has got here but it hasn't worked out and he has taken full responsibility for that.
"He knew that first team results weren't anything like as good as we had hoped they would be and he agreed that the change had to be made."
Steve Agnew will take charge of the team while the club seek a successor to the Scot.
"We are now working on a shortlist of potential candidates as Gordon's successor. It is crucial we put the right man in charge so I will not rush into a decision," said Gibson.
"First of all, we have an important league game on Tuesday night. With that in mind, Steve Agnew has been given responsibility for all first team matters until a new manager is appointed."
