With Murphy's inauguration, New Jersey joined a handful of states where Democrats control both the governor's mansion and the legislature.
The crowd roared as Murphy praised immigrants who help build a better future in the state, "and that includes from Haiti and continent of Africa".
Murphy set an inclusive tone for his administration - pointing to his diverse senior staff standing on stage behind him, among them the nation's first Sikh attorney general, Gurbir Grewal - and said the public had "rejected the politics of division".
Trump called Murphy and new Democratic Virginia Gov. Ralph Northam on Sunday to congratulate them.
A federal transportation official said last month that an earlier agreement with the Obama administration for the federal government to pay for half of the project is "non-existent".
Surrounded by his family, Murphy - a 60-year-old Middletown resident - was sworn in by state Supreme Court Chief Justice Stuart Rabner in the midst of a festive ceremony.
Minutes later, Murphy - who beat Republican Kim Guadagno, the outgoing lieutenant governor, in November's election to win the job - outlined how he would roll back many of Christie's policy decisions, from defunding women's clinics to backing off climate change efforts.
"The work of our administration will be about you, your families, and your communities", Murphy said at the Trenton War Memorial near the Statehouse.
Murphy thanked him for over two decades of public service to the state.
"As our infrastructure goes, so goes the state", he said, adding New Jersey is the fourth smallest state geographically, and the densest state in the country.
"To my partners in the Legislature: I ask you to send me the bills, among others, to reaffirm our support for women's health and Planned Parenthood; to raise the minimum wage to $15 an hour; to promote equal pay for women; to give every worker the peace of mind of earned sick leave; to tear down barriers to voting; and, to strengthen our gun laws", Murphy said. The state's last Democratic governor, Jon Corzine, who Christie ousted in 2009, was also an executive at Goldman Sachs.
Murphy has never held political office and earned his fortune, which he used to help win the Democratic nomination a year ago, as an executive at Goldman Sachs.
He takes over from a larger-than-life governor who oversaw the state as its economy rebounded but who also saw his popularity plunge after a failed presidential run and the George Washington Bridge lane-closure scandal.
The former Wall Street executive and USA ambassador to Germany will become the state's 56th governor after he is sworn in at the War Memorial in Trenton.