The striker's U-turn is a significant fillip to the club who have been insistent all summer that the forward will not be sold at any price.
"For now, because of all the affection of the people, I will be staying," Suarez told El Observador from Tokyo, where the Uruguay national side are set to face Japan.
In a saga that looked likely to drag on all summer, Suarez had claimed the club had broken a promise to him that he could leave after their failure to secure Champions League qualification.
That claim was met with a stern response from Liverpool with manager Brendan Rodgers stating that the striker would have to apologise to his club and team-mates if he wanted to be welcomed back into the squad.
"Initially there will be an apology to his team-mates and the club, then a recognition that he is ready to fight for the club," Rodgers told reporters after Liverpool had lost to Celtic in their final pre-season friendly in Dublin on last Saturday.
While the apology has yet to be forthcoming, Suarez's decision to put on record with respected South American journalist Martin Charquero his desire to remain at the club will be seen by many as a first step in that rehabilitation process.
Charquero tweeted to say Suarez had informed him he would not be leaving Liverpool, before the striker went public when speaking to El Observador.
The news will come as a blow to Arsenal who had made the former Ajax man their primary transfer target after missing out on Gonzalo Higuain, who joined Napoli from Real Madrid, but Suarez's decision marks a significant victory for owner John W Henry.
As the Uruguayan's relationship with Liverpool has deteriorated rapidly over recent weeks, American Henry was adamant Suarez would not be sold to Arsenal - despite their bid of £40,000,001 on July 24 that the player and the London club thought triggered a clause that meant the Reds had to negotiate.
Henry's original reaction to the bid was one of incredulity:
But as Arsenal's interest intensified, he took a more serious tone.
"We are not going to sell Luis. It's a football reason, it's not about finances," Henry said.
"It's because at this point it's impossible, so late in the window, with everyone who's already moved or isn't moving, to replace him. So for football reasons, we can't - and especially to Arsenal.
"For all the top clubs it's extremely important but especially Liverpool because we're not in Europe this year and have not been in the Champions League for a while.
"Obviously, to sell to a rival for one of those positions would be ludicrous."
Such was the Uruguayan's determination to leave Anfield it was thought he was willing to take some form of legal redress to push the move through but that stance was dealt a near fatal blow when PFA chairman Gordon Taylor said it was "practically impossible" for Suarez to leave Liverpool this month - an outcome the player appears now to have accepted.
Sent from my BlackBerry® wireless handheld from Glo Mobile.