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.
The woman chosen to succeed Gerry Adams as leader of Sinn Fein has described her rule as a "defining chapter" in Irish nationalism.
Deputy McDonald's succession to president-elect comes after Gerry Adams a year ago announced he would be standing down as his party's leader in 2018.
Blevins said: She's not a woman who anyone would want to take lightly.
The Dublin TD, 48, told Sinn Fein's Ard Chomhairle this morningshe that she felt an "enormous sense of pride" at receiving the nomination to be president elect.
A special party conference will be held on 10 February to ratify the new leader.
McDonald became a member of the European Parliament in 2004.
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?".
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Kylie and sister Kendall were mysteriously absent from the event and so Khloe was seen FaceTiming Kylie to tell her the news. She says that being under anesthesia for a long period of time scares her.
Fiachra McGuinness, son of the late Martin McGuinness, tweeted a video message declaring he was "proud and honoured" to endorse Ms McDonald.
He described politics in Northern Ireland as "very polarised and very toxic". "It is my view that this does not help anyone except a small minority of bigots", he said.
A fresh talks process aimed at restoring the power-sharing government at Stormont is due to begin on Wednesday.
Several rounds of talks aimed at ending the political stalemate ended without agreement.
Mr Adams also said a united Ireland was not a "pipe dream", adding: "It is very achievable - we can do it".
"We have to challenge ourselves and our support base".
She also said: "I believe we are capable of achieving anything that we set our minds to".