"Hard work and tough decisions will be required of the 112th Congress," Boehner said. "No longer can we fall short. No longer can we kick the can down the road."
Voters on Nov. 2 "humbled us," reminding lawmakers "just how temporary the privilege of serving is," Boehner said. "They have reminded us that everything here is on loan from them."
Administering the oath of office to Boehner was Rep. John Dingell, D-Mich., the longest serving member. The oath traditionally is administered by the longest serving member.
"Our aim will be to give government back to the people," the new speaker said, and will "part with some of the rituals that have come to characterize this institution under majorities Republican and Democratic alike."
He said he wanted to dispense with the conventional wisdom that "bigger bills are always better, that fast legislating is good legislating," and that "allowing additional amendments and open debate makes the legislative process 'less efficient' than our forefathers had intended."
He said legislation coming through the House would be more focused, better scrutinized and constitutionally sound, and committees would be smaller and have more oversight.
It also will be easier to cut spending, he said, "and we will start by cutting Congress's own budget."
Boehner said he welcomes the "battle of ideas" but warned both sides they must respect each other and begin to rebuild trust within the chamber and with the American people.
"In time, I believe this framework will allow the House to be a place where people's work is done," he said, rebuilding trust and providing a guidepost for members in years to come.
If representatives brace themselves to do their duty and "do what we say we're going to do, I don't think there's anything we can't accomplish for the people we serve," Boehner said. "Welcome to the people's house. Welcome to the 112th Congress."
In her farewell speech, Rep. Nancy Pelosi, D-Calif., now minority leader, said all members "recognize the proudest title we will ever hold ... is the simple title of 'American.'"
She recounted successes under her watch, including passage of healthcare and Wall Street reforms, improved conditions for veterans, equal pay for equal work and repeal of the military's "don't ask, don't tell" policy barring gays and lesbians from openly serving in the military.
Democrats, she said, "will judge what comes before (the House) on whether it creates jobs, strengthens the middle class and reduces the deficit."
"When the new speaker of the House and (the new) majority come forward with solutions that address these challenges, you will find us a willing partner," she said. "As we wish them success ... we stand ready to find common ground, to solve problems and to build a more secure future for all."