Rangers are yet to find a replacement for Pedro Caixinha and have been chasing McInnes for some time.
The former Rangers midfielder spent two days in negotiations with Dons chairman Stewart Milne after Aberdeen rejected an approach for the Ibrox club on Tuesday evening.
Rangers have since released a statement expressing their frustrations at failing in their pursuit to convince McInnes to join.
But after six weeks without a manager, Rangers will have to look elsewhere after McInnes confirmed he would be staying with Aberdeen.
McInnes told his club’s Red TV channel: “It’s been a challenge for everybody concerned over the last wee while. I had something to consider, as it is in life.
“If you are deemed to be doing well, you normally get opportunities and offers and decisions to make.
“But I wasn’t prepared to walk away just yet. I am really happy here as everybody knows, and I wasn’t prepared to tarnish relationships that I have built over the last wee while.
“Hopefully everything gets settled down. None of this has been of our own doing. Since the official approach was made on Tuesday we quickly got it put to bed.”
McInnes and assistant Tony Docherty missed two days of training immediately before their Friday night trip to face Dundee and the 46-year-old now wants total focus on the football.
Aberdeen have dropped 11 points since McInnes was installed as the favourite to replace Caixinha, a run which included two defeats against Rangers last week.
“We want to get back to normal practice,” he said ahead of the trip to Dens Park. “We have tried to be as normal and professional as possible throughout it. I don’t like when we don’t win games. Ultimately that’s why there has been a bit of a cloud.”