Parker's public inauguration was held at the Wortham Theater on Monday.
Several former mayors, including Bill White, Lee Brown, Bob Lanier, Kathryn Whitmire and Fred Hofheinz were in attendance.
The inaugural program featured talented Houstonians, including Barbara Padilla, who led the national anthem. Joel Osteen, pastor of Lakewood Church, gave the invocation.
U.S. District Judge Vanessa Gilmore administered the oath of office to Parker. Parker's life partner, Kathy Hubbard, held the Bible during the ceremony.
"I do love this city," she said. "I think you've heard that before, but I can't stop saying it."
Parker is Houston's second female mayor and 61st overall.
"I want to thank all Houstonians for honoring me with your trust and your hopes for the future," Parker said. "To serve this city has been my highest aspiration. To work with you on the pressing issues and challenges we face is my mission. I will respect the office and I revere the oath I have taken."
Gilmore also administered the oath of office to City Controller Ronald Green.
Parker administered the oath of office to 14 City Council members.
"I want to congratulate our new City Council members and the controller," Parker said. "Having served in both of those positions, I know the challenges and opportunities that they face. I salute their service to our city. This is a good council, truly representative of our city and its diversity."
Parker, 53, was sworn in as chief executive of the United States' fourth-biggest city in a private ceremony on Saturday. She said she opted for a private ceremony on the weekend to avoid overtime costs that would be incurred if the public inauguration was held on the weekend.
The ceremony was held to meet the legal requirements of the City Charter, which mandates that the transfer of power occur on Jan. 2.
Green was also sworn in during Saturday's private ceremony.
Parker took almost 54 percent of the vote in a runoff last month, defeating former city attorney Gene Locke in a race to succeed term-limited Bill White.
The three-term former city controller has never made a secret or issue of her sexual orientation in any of her runs for office. Her lifestyle did draw attention after anti-gay activists and some religious groups endorsed Locke and sent out mailers condemning her.
"I spoke on election night of that being an historic election, and my election made news all around the world," she said. "Now, Houstonians weren't very surprised they elected a gay woman. We have a tradition of electing mayors not for who they are but for what they believe we can do as a city."
Parker addressed some of her inaugural remarks to the city's gay, lesbian, bisexual and transgender community specifically.
"I understand how much this day means to you," Parker said. "I can feel your excitement and your joy. I can also feel your apprehension and longing for acceptance. I will gladly carry you forward, but today is simply one step toward a tomorrow of greater justice. When the time comes, I will gladly pass the torch to the next in waiting and I will cheer for them as you do for me. Your bravery in the face of threat, your grace in the face of insult sustains me. We will support each other."
Several smaller U.S. cities, including Portland, Ore., Providence, R.I., and Cambridge, Mass., have openly gay mayors.
Parker takes over a city of 2.2 million that's weathered the national recession better than most but still is facing what she's estimated as a budget deficit of about $3 million.
"Every speech by every mayor in this country these days will discuss the economic downturn," she said Monday. "In truth, the quality of life in many cities is not what it was four years ago.
While acknowledging a budget shortfall, "We will not let that happen to the city of Houston," she said.
Parker inherits unfunded pension-fund commitments for police, firefighters and other city workers, sagging revenues from water and sewer operations that may require rate increases, and a campaign promise to overhaul the police department whose chief quit last week and whose largest union representing officers endorsed Locke. She'll also need to replace the chairman of the board that oversees Metro, the city's public transit agency.
After the inauguration ceremony, Parker and all the council members went over to City Hall for their first council meeting.
An inaugural celebration will be held at Discovery Green at 6 p.m. There will be several performances and fireworks.