Republican Gov. Rick Snyder was expected to sign both bills, despite stiff opposition from Democrats and unions. The laws would become effective April 1.
The two bills opposed by all Democrats and some Republicans, were enacted within three hours of each other, The Lansing State Journal reported.
However, the newspaper said, one of the bills might be reconsidered in the House Wednesday, and that might delay Snyder's signature.
The House approved Senate Bill 116, right-to-work legislation for private sector workers, by a 58-52 vote. That vote came about an hour and a half after the House approved House Bill 4003 giving public sector workers right-to-work protection.
The legislation would end rules forcing workers to pay union fees as a condition of employment.
Outside the Capitol, a crowd of protesters swelled to 10,000, as demonstrators pounded drums and emptied buckets, The Detroit News reported.
A large pro-union rally was held in front of Lansing's City Hall and giant loudspeakers broadcast speeches across the Capitol lawn, the report said.
United Auto Workers President Bob King was among the speakers.
"Unions built the middle class of America. This is a national attack," he said. "These folks want to shift more and more of the wealth to a smaller and smaller group of people."
The News said the speakers included firefighters, teachers and factory workers, who promised Tuesday's protest was just the start, and said they would follow legislators all over the state to remind the public of their votes.
Earlier Tuesday, police used chemical spray Tuesday on the east side of the Michigan Capitol after a crowd pushed toward the building.
The clash was a sign of increasing tension as legislators considered the bills.
The State Journal said Michigan State Police troopers in face shields joined mounted police from the Clinton County Sheriff's Department to keep back the crowd, where some shouted: "A union united will never be divided."
The newspaper reported witnesses said mounted police tried to push the crowd back, and at least one protester was knocked down. State police confirmed at least one man was sprayed, and said they are investigating.
The Capitol was closed after officials said the building had reached its capacity, leaving thousands of union members on the lawn outside, The New York Times reported.
Streets around the Capitol were closed to traffic, the Times said, while state police, some carrying riot gear, stood guard throughout the building and along nearby streets.
Protesters began arriving as early as 5 a.m. carrying supplies to help them stay warm during a day that started with chilly 22-degree weather, the News reported.
Unions fear the legislation could undermine their political presence, their membership numbers and their clout. They also fear a drop in wages.
Three school districts closed for the day as too many teachers had called in sick to attend the rally to keep classrooms staffed.
"We're encouraging our members to stand in solidarity as a show of anger, defiance and frustration for this whole Legislature," Detroit Federation of Teachers President Keith Johnson said.
"It is only designed to break unions and has noting to do with workers," he said.
"They're trying to destroy public schools and close down public services, which are the backbone of the state," said teacher Steve Conn at Cass Tech High School.
Advocates of right-to-work say it gives employees and employers more freedom.