Daniels and Republican supporters say the measure will attract jobs to the state, while opponents say it will depress wages.
"The only change will be a positive one," he said in a statement. "Indiana will improve still further its recently earned reputation as one of America's best places to do business, and we will see more jobs and opportunity for our young people and for all those looking for a better life."
The law bans companies and unions from negotiating a contract requiring non-members to pay fees for the representation unions are required to give them. Opponents of the measure said the law will allow workers to get union benefits without paying for them and will ultimately reduce wages.
"This law won't be a magic answer but we'll be far better off with it," Daniels said. "I respect those who have objected but they have alarmed themselves unnecessarily: no one's wages will go down, no one's benefits will be reduced, and the right to organize and bargain collectively is untouched and intact."
The Indiana Senate voted 28 to 22 Wednesday to pass the bill as thousands of protesters packed the Statehouse shouting their disapproval, The Indianapolis Star reported. Union protesters marched from the Statehouse lawn into the Super Bowl Village shortly after the vote.
Indiana is the 23rd state with a so-called right-to-work law and the first to adopt the law since Oklahoma in 2001.