The fluently bilingual Quebecer is the first to formally enter the race to succeed Layton, who died last month from cancer.
"No one can replace Jack," Topp declared at a news conference today.
"But we can honour him by making sure his dream of social justice will never die. We can carry on his work. That's my pledge today.
"I'm seeking the leadership of the New Democratic Party of Canada and I pledge to continue to build our party on the strong foundations that Jack built."
Topp was joined by former NDP leader Ed Broadbent and Gatineau, Que., MP Francoise Boivin.
Topp's name surfaced early as a possible contender in the NDP leadership race. The fully bilingual Montrealer has worked in NDP backrooms for years, and was a close confidant of Layton.
Layton led the New Democrats to unprecedented success in the May 2 federal election as the party surged to official Opposition status for the first time, winning 103 seats, including an astonishing 59 in Quebec.
Topp noted nearly 60 per cent of Canadians did not vote for the Tories, and said replacing Conservative Prime Minister Stephen Harper was "a piece of unfinished business.""I'll lead a caucus that works harmoniously and seriously as a government-in-waiting," he said. "And then, we'll win. And then, we'll govern well."
He said he will expose Harper's "failed record" before winning the next election and forming Canada's first NDP government in Ottawa.
"And that day will be a great day, a new dawn for every Canadian across this country."
Broadbent, who nominated Layton for the leadership eight years ago, said he is backing Topp as the most qualified candidate.
"Now we need another builder, one who will take us from leader of the official Opposition to the Prime Minister's Office," Broadbent said.
"While there will be a number of good candidates — and I believe there will be — there is no one who stands clearly above all the others in the qualities that matter most.
"Brian Topp is that person. He has the political and intellectual substance we need to meet today's challenge. He has the qualities Canadians need in a prime minister. He is ready now."
The NDP is set to hold a caucus retreat starting Tuesday in Quebec City.
Other potential candidates include deputy leader Thomas Mulcair, the party's Quebec lieutenant; along with MPs Peter Julian, Charlie Angus, Paul Dewar, Robert Chisholm, Nathan Cullen, Romeo Saganash, Megan Leslie and Peggy Nash.
The leadership convention is scheduled to be held March 24 in Toronto.