It is the SDLP's turn to hold the position and the party nominated the north Belfast councillor last week.
The decision was ratified at a full meeting of Belfast City Council on Monday night.
Maire Hendron of the Alliance Party has been elected deputy mayor - the first time women have held the two top posts.
Ms Mallon, 34, said being chosen as lord mayor was a tremendous honour.
"I want to congratulate Máirtín Ó Muilleoir on a fantastic year in office and thank my own party for nominating me to take on such a privileged position," she said.
"I have had the privilege of representing the Oldpark area, the place I grew up in, for the last four and a half years.
"The most wonderful part of being a councillor, for me, continues to be the many unsung heroes I get to meet - all those people who through their compassion and selflessness, makes this city the special place that it is."
She said she wanted to take the lord mayor's role "out of city hall and into people's lives".
"I want to connect with those who at times feel invisible in our city. I want to celebrate and showcase our unsung heroes who really are Belfast's first citizens," she said.
"Belfast is a city for everyone, where everyone belongs and where we are all the better for having each other."
Ms Mallon is only the third woman to hold the office of lord mayor of Belfast, following the Ulster Unionist Party's Grace Bannister in 1981 and Naomi Long of the Alliance Party in 2009.
With Lydia Patterson of the DUP also serving as high sheriff, it is the first time that all three civic dignitaries in Belfast are women.
After her appointment, the city's new deputy lord mayor said she was "looking forward to the year ahead".
Ms Hendron added: "During my year in office, I would hope to play my part in building a more inclusive city that is open to all.
"I want to work with all groups from different backgrounds to further improve Belfast's diversity, which is a source of strength for our society."

Under the plans announced by Chancellor George Osborne in July, the minimum wage for over-25s will rise from £6.50 an hour to £7.20 in April next year.
It will rise to at least £9 by 2020.
The Scottish government said the proposals were "simply an enhancement of the national minimum wage" rather than a true living wage.
Its Fair Work Secretary, Roseanna Cunningham, also argued that the plan discriminated against under-25s and will bring further complications and inequalities to the national minimum wage structure.
But a UK government spokesman said its proposals were an "essential part of moving to a higher wage, lower tax, lower welfare society where work always pays and the majority of households are better off."
Ms Cunningham has outlined the Scottish government's criticisms in a submission to the Low Pay Commission's consultation on the proposals.
And she called on the UK government to set out a clear plan for moving towards a living wage that "truly reflects the cost of living" rather than merely setting an "arbitrary rate".
Ms Cunningham added: "The so-called national living wage announced in the UK government budget is not a living wage and should not be referred to as such.
"It is simply an enhancement of the national minimum wage which disgracefully discriminates against the under 25s.
"Employers also do not need further complications in the national minimum wage structure and I would encourage all bodies looking at this to ensure that younger workers are treated fairly."
The Scottish government promotes a living wage of £7.85 an hour, with businesses north of the border encouraged to sign up to a voluntary accreditation scheme.
Ms Cunningham said: "We are working hard to increase the number of employers paying the living wage. By this I mean the real living wage, which is calculated according to the cost of living.
"There are now over 300 organisations across Scotland that recognise the tangible benefits to their business of being accredited, huge progress in the last 12 months."
In response, the UK government spokesman said its proposals were expected to directly boost the wages of nearly three million people and would mean a full-time worker would earn £2,000 more per year by 2020.
He added: "For younger workers, the priority is to secure work and gain experience.
"In order to maximise the opportunities for younger workers to gain that experience  the national living wage will only apply to workers aged 25 and over.
"The wages of younger workers will continue to be underpinned by the core national minimum wage."
The SDLP's Nichola Mallon has become the new lord mayor of Belfast, succeeding Sinn Féin's Máirtín Ó Muilleoir.
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The UK government's National Living Wage plans have been criticised as a "misappropriation of the term" by the Scottish government.