Dubliln based Mary Lou McDonald is set to become the new leader Sinn Féin.
Mr Adams, a pivotal figure in the political life of Ireland for nearly 50 years, announced he would step down as leader of the former political wing of the Irish Republican Army (IRA) last November after more than three decades in charge.
Ms McDonald said she grew up watching Mr Adams on the television and could never have imagined she would one day replace him as leader.
Speaking in Belfast, the president-elect told supporters that Irish unity was "the best solution, the best collective arrangement" and that she believed it could be done "in an atmosphere that isn't toxic or bigoted...but is...respectful".
The Dublin Central TD was the only person to put her name forward for the role as party' leader before nominations closed on Friday.
"I know I have big shoes to fill taking on the role from Gerry Adams and I know that is impossible", McDonald said.
She said her primary concern would be uniting Ireland: "Uniting this island is the best outcome for all our citizens and it is now our task to convince our unionist friends and neighbours of that and to encourage them to help us build a new Ireland".
A Claire Byrne/Amarách poll for the TheJournal.ie asked people: "Would you be more likely to vote for Sinn Fein under the leadership of Mary Lou McDonald?"
I am proud and honoured to be nominated for Uachtarán Shinn Féin. "We also need to win that referendum. don't believe the naysayers and begrudgers who claim that a United Ireland is a pipe dream".
He said his father was a "huge admirer of her ideas, dedication and commitment", and that she was the "ideal candidate to lead Sinn Fein into the future". "Leadership means knowing when it is time for change and that time is now", said the 69-year-old Adams at the time.