The new law asks state procurement officials to give preference in bids for such services to contractors employing workers only in the United States. It was approved overwhelmingly by lawmakers last month and signed into law last week.
"It is significant because it is the first time for a state to do preferences for data-entry and call-center work through legislation," said Justin Marks, a policy analyst for the National Conference of State Legislatures.
The bill was filed in response to the growing controversy over outsourcing of white-collar jobs to India and other countries with large populations of educated English speakers willing to work for significantly less money.
Legislatures in 35 states have introduced bills seeking to address the issue, usually by banning the state from contracting with companies planning to employ offshore workers. Intense lobbying by business groups has helped prevent passage of those bills in other states.
Business groups say a ban would be illegal and could prompt other countries to retaliate by preventing U.S. companies from doing business with foreign governments.
The original bill in Tennessee sought to ban the state from contracting with companies employing foreign workers, but it was watered down.
The legislation doesn't affect existing contracts and is vague about how much preference should be given to bidders who hire only U.S. workers, leaving that task to the state's commissioner of finance and administration.
Lola Potter, a spokeswoman for the department, said the most likely answer would be granting extra points to contractors under the scoring system used to determine bid winners.
"We'll have to try to find a way to make that happen," she said.