In her first speech as president, Ms McDonald is expected to set out an ambitious agenda to modernise the party, getting it into government in the Republic of Ireland, and Northern Ireland, to bring about the goal of a united Ireland.
The talks will be on hold over the weekend as Mr Adams steps down as Sinn Fein president at the party's special ard fheis in Dublin.
However, the new party leaders face a number of challenges - such as the continuing struggles to reach agreement on restoring the Northern Ireland Executive.
Sinn Féin is among the top political parties in Ireland as well as Northern Ireland.
He was questioned in 2014 about the disappearance of Jean McConville, 38, a widowed mother of 10 who was abducted by IRA gunmen in 1972 and found buried on a beach in 2003.
She became the party's Deputy in 2009 and in 2011 won a seat in the Irish Parliament, representing Dublin Central.
"The outcome of Brexit is that people have just been reminded that for the last 20 years we have just practically had a single island economy, the border has ceased to be the intrusive, in your face, structure - it is still there of course and we want rid of it in any form - but people have just been reminded how good that has been".
He said this was largely due to the growing spotlight on the Irish border, which has been invisible both in terms of infrastructure and customs checks since the Good Friday Agreement in 1998.
49ers Make Jimmy Garoppolo Highest Paid Player In NFL
Likely, offensive line additions and potential big-name receiver are on the 49ers' - and Garoppolo's - wish list. That average annual value is massive, and it will set the market for contract deals moving forward.
Although Sinn Fein has in recent years used a strong roster of candidates to build electoral support in the Republic of Ireland, some southern voters who would otherwise be attracted to its broadly center-left policies are still troubled by its previous support for IRA violence under Adams's presidency.
However, unlike Martin McGuinness or Gerry Kelly, she had no direct IRA involvement. There is no value in engaging in the blame game. And as we become more multicultural it is also about making space for all of those other folks out there who wouldn't be part of the orange and green tradition.
Michelle O'Neill has also been formally been elected as Vice president of the party.
Today marks the high point of Ms Lou McDonald's political career.
Regarding social issues, she said that Sinn Fein will campaign enthusiastically for the repeal of the Eighth Amendment of the Constitution of Ireland, which virtually bans abortions in the country.
Ms McDonald added: "We do not have to agree on the past". That could be a tricky position given that Sinn Fein draws much of its support from Catholic communities. "We are the generation of republicans who will see the rising of the moon", she said on Saturday.
"There is now a peaceful and democratic path to Irish unity".