The 33-year-old, who has scored 51 goals in 106 internationals, said on Monday he had quit “permanently” after being replaced as captain.
President Nana Akufo-Addo spoke to Gyan on Tuesday, prompting the Kayserispor striker to change his mind.
“A presidential request is one that cannot be disregarded,” he said.
“I have taken the request in good faith, and will make myself available for selection by coach Kwasi Appiah.”
On Wednesday, Ghana are due to name their provisional squad for the Africa Cup of Nations in Egypt, with Andre Ayew likely to be captain.
Gyan has not featured for the national side since September 2017 after persistent injury problems, and has also struggled for game-time at Kayserispor.
He said his desire to help Ghana win AFCON “still burns strong” and he remains “committed to serving this great nation and the people of Ghana”.
Gyan has scored at six consecutive Nations Cup finals, as well as three World Cups between 2006 and 2014.
Concise News had reported on Monday that Gyan, who has been with the Black Stars for 16 years shared a statement titled, “Decision to recuse myself from AFCON 2019, Egypt and retire from the national team”.
Part of his statement read, “I cannot pretend to be happy. I would rather hurt myself emotionally and psychologically, over the years I served with an open heart and have given my all to the best of my ability in my quest to serving our great nation, Ghana. I have represented the proud colours of our country in 10 major tournaments from the Olympics, World Cups and in African Nations Cups with different coaches.
“In all, I would say the last years have been the proudest moments in my career as a captain under the managerial leadership of coach Akwasi Appiah. I stood solidly behind my coach during the difficult times in Brazil and in some cases supported the endeavours of the team financially when the need arose to make sure his tenure and my captaincy would not suffer challenges and to ride with the assertion, ” A Ghanaian coach can do it.
“My team, my family and fans have had reasons to whisper the trend of reportage and articles either to substantiate my exclusion or inclusion and again rumoured roles I am to play at the AFCON in Egypt. In all, my answers have been, “respect the decision of the coach because the records under the year per game minutes and goals for all attackers are evidence to guide his decision”.
“Upon consultation with my family and team, and as an active footballer and captain of the national team, if the decision of the coach is to give captaincy of the tournament to another player while I am named in the team of the tournament.
“I wish to recuse myself from the tournament. I also wish to retire from the national team permanently; not pretending my presence would not fuel the purported undermining the country has seen under my captaincy.”