Erdogan won the vote to be Turkey's first elected head of state on August 10, replacing Gul with whom he founded Turkey's ruling Justice and Development Party (AKP).
Political commentators had claimed that Gul had been frozen out of a possible return to government by Erdogan and his supporters as the president-elect further tightens his grip on power.
"As far I understand, Ahmet Davutoglu will be the next head of government," the outgoing president told the media at his last reception at the presidential palace in Ankara.
"We must all help him with his task. It was I who convinced him to go into politics. I am going to support him," said Gul of the understated former academic, who has been foreign minister since 2009.
Erdogan's first-round victory in the presidential poll cemented his status as the most dominant figure in Turkish politics since Ataturk.
He is set to officially name his successor on Thursday. Davutoglu, an Erdogan loyalist, is unlikely to challenge the president-elect's vow to be a powerful head of state.
The new premier will first have to be elected party leader at a special AKP congress called for August 27, before taking office and forming a government.
Gul, however, took a swipe at those who had shown him a "lack of respect" in opposing him retaking a leading role in the party.
While he said he does not intend to return to frontline politics, he repeated that "it is natural to return to my party".
Gul founded the AKP with Erdogan in 2002, the year before it won the first of its three general election victories, before cutting ties with the party to become president in 2007, as the constitution demanded.
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Can anyone name a single foreign policy accomplishment credited to the Foreign Minister? The harsh reality is that he is known for dressing in expensive suits and chasing microphones/cameras/press conferences - not much more. Turkey deserves better.
I do not trust Erdogan or the people who support him so blindly, I think if he get's the power he so badly want's and he get's all the changes to the Turkish constitution he is after Turkey will become an Islamic country once again and not a secular one and all that Ataturk and his followers did will be forgotten. I have notest Erdogan always use's what we in the UK call the Royal "WE" not I or me but "WE" the same as the UK's Queen dons in her speeches. In the past the Army would have go in and put things right but Erdogan has made certain the they can no longer do that, it is sad for the Turkish people who did not vote for him, they do not want to see Turkey become an Islamic country and not a secular one.