He put his signatures on the bills today, hours after the state House passed the measures.
Mr. Snyder says a failed ballot proposal to enshrine collective bargaining rights in the constitution triggered the discussion that led to the passage and signing of right-to-work.
During a news conference, he called the protests "an exercise in democracy."
Earlier today, the Michigan House today approved two contentious right-to-work bills limiting unions’ power as a boisterous but mostly peaceful crowd of thousands surrounded the Michigan State Capitol.
The bills were passed by the Michigan Senate last week.
Michigan becomes the 24th state with right-to-work laws, which give workers a choice on whether or not to join a union and ban requirements that nonunion employees pay unions for negotiating contracts and other services.
Earlier today, the Republican-dominated House first passed a measure dealing with public-sector workers 58-51 as protesters shouted “shame on you” from the gallery and huge crowds of union backers massed in the state Capitol halls and on the grounds.
Democrats immediately sought to have the vote reconsidered but failed in that effort.
The House then passed a second bill dealing with private-sector workers.
Outside the Capitol, protesters beat makeshift drums, rang cowbells, and chanted pro-union slogans.
After word of the first vote, close to half of the crowd disappeared. At its peak, the crowd was estimated at more than 10,000.
Mike Ingels, a teacher at Addison Community Schools in Adrian, said the legislation is an attempt to destroy the opposition.
He vowed to keep fighting, no matter what happened today.
“This is not the end,” he said. “This is the beginning.”
Backers say a right-to-work law would bring more jobs to Michigan and give workers freedom. Critics say it would drive down wages and benefits for all workers.
Supporters of the legislation say Indiana was opened up to more economic opportunity after passing right-to-work legislation earlier this year.
But Bob Cebina, president of Monroe-based UAW Local 723, has his doubts.
“I would like to see the data on what kind of benefits they give those people and what kind of wages they’re paying them.”
Local 723, headquartered in Monroe, represents about 2,200 people at several plants in southeast Michigan. Mr. Cebina said about 60 members of his local made the trip either by bus or by carpool.
Michigan State Police said pepper spray was used to subdue one protester outside the Capitol who had his hands on a trooper.
Capt. Harold Love says the female trooper was being pulled into a crowd Tuesday. Love says a male trooper standing nearby gave two short bursts of pepper spray to end the incident. There was no arrest.
Captain Love says two people were arrested when they tried to get into the George Romney Building, a state office building that was closed.
On the Capitol grounds, a big white tent erected for supporters of the legislation collapsed. There were no injuries.
The Associated Press contributed to this report.