Gerrard said on Tuesday he had made the toughest decision of his life to leave his first and only club six weeks after lifting the Champions League trophy in Istanbul.
The England midfielder will now sign a new contract on Friday, SkySports news reported.
"I just couldn't leave the club I love," Gerrard told Liverpool's website.
"I had the whole of yesterday to think about my decision and what I was doing. I turned off my phone and my television and went through it all in my head again.
"After considering everything that's gone on, I just couldn't go through with it and leave this club.
"I love Liverpool so much. This is my club. My heart is with Liverpool."
After making his u-turn Gerrard offered to give up the Liverpool captaincy, an offer turned down by manager Rafa Benitez.
SAME IDEA
"It is true that he offered to give up the captaincy but I spoke to some players and our idea was the same -- that Stevie should be our captain," said Benitez.
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Earlier on Wednesday Parry said that in a series of telephone calls he had apologised to Liverpool-born Gerrard for any misunderstandings about the club's desire to keep their talisman.
Newspapers reported Gerrard had been upset by the slow pace of his contract negotiations since the Champions League win over AC Milan.
"We've cleared all of that and I don't think it will happen again. It hasn't been easy for him but as far as we are concerned it is the right decision," said Parry.
The five-times European champions rejected a bid for the 25-year-old from Premier League champions Chelsea earlier this week. Newspapers reported Chelsea had bid a British record 32 million pounds ($56.28 million).
Gerrard's change of mind is a carbon copy of the situation 12 months ago when the player appeared set to join Chelsea, only to follow his heart and stay with his hometown club.
Gerrard scored one goal and made another against AC Milan when Liverpool rallied from 3-0 down to reach 3-3 and a penalty shootout victory after extra time in the Champions League final.
Liverpool are preparing to face Welsh part-timers TNS in their Champions League first round qualifier on July 13.