NEW ORLEANS—Barrett Conrad had plenty of chances to leave this city after earning a degree in computer science from Tulane University in 2002.

Instead, the creator of a smartphone app for trivia buffs now urges computer programmers from across the country to move here.

“Everybody I know is hiring,” said Mr. Conrad, a fast-talking, 32-year-old Arkansas native with thick-rimmed glasses who works out of a sparse office in the city’s Central Business District. “And if they aren’t, give them three months.”

New Orleans is in the midst of a mini tech boom, as young “nerds with laptops” are moving from New York, San Francisco and elsewhere to staff established digital businesses and start-ups, said Chris Schultz, the 37-year-old co-founder of Launch Pad, the New Orleans tech incubator where Mr. Conrad rents a desk to work on the company he founded, Red Ticket Games Inc.

A metric of technology jobs generated by Moody’s Analytics—a broad category that includes everything from pharmaceuticals manufacturers to software publishers—shows New Orleans’s stock of tech jobs grew 19% from October 2005 to April 2012, compared with 3% nationwide.

Companies from start-ups to large established entities are expanding or setting up shop here, drawn by a state tax credit that is offered to digital-media and software firms.

Between 2008 and 2010, 69 projects qualified for the tax credit, according to BaxStarr Consulting Group LLC, up from five between 2005 and 2007. The tax credit covers 25% of companies’ production costs and 35% of payroll expenses for employees who live in Louisiana.

The tax credits appeal in particular to smaller tech companies because they can be sold on an open market, Mr. Conrad said. Under state law, the credits a company accumulates can be transferred to any Louisiana taxpayer. A company that doesn’t need its credits—for instance because its tax liability is smaller than the credits—can sell them at a lower price, with the buyers using them to reduce their taxes.

The new tech talent pool brought in by smaller firms has started to draw larger companies, such as Paris-based Gameloft SA, a company specializing in downloadable games for mobile phones that opened a design studio in New Orleans last year.

Last summer, GE Capital, General Electric’s financial-services unit, set up its information-technology offices here and plans to hire as many as 300 people in the next three years, at salaries from entry level to six figures.

Mike De Boer, who runs the GE Capital IT office here, said his company decided to skip the tax credit, though it did get other incentives to move to Louisiana. The key reason to move, he said, was the city’s growing talent pool. “Our goal is to take advantage of what’s going on,” said Mr. De Boer, who just moved New Orleans from France.

Whether the tech community can continue to grow in a city that struggles with revenue and infrastructure problems and has one of the highest per capita murder rates in the nation remains to be seen. Mr. De Boer said he believes many long-standing problems, including crime, infrastructure and schools, are being tackled by local and state government. “There are a lot of efforts under way to fix those issues,” he said.

Louisiana’s higher-education budget has decreased since 2008, but tech companies are working with schools to produce graduates with skills the firms need. GE Capital is collaborating closely with the University of New Orleans, as well as private universities such as Tulane, and also seeks to recruit staff from across the South to New Orleans, Mr. De Boer said.

The burgeoning tech sector is a small part of a broader rebound in Louisiana’s economy after a string of calamities, from hurricanes Katrina and Rita in 2005 to the Deepwater Horizon oil spill in 2010. Much of the growth has been due to the state’s traditional economic drivers: oil and gas, chemicals and tourism. Oil production off Louisiana’s coast is booming and natural-gas companies have been expanding in shale areas in the northwest part of the state. Tourism, which took a huge hit from the hurricanes and the recession, has rebounded.

At least $50 billion in various industrial construction projects in Louisiana—almost all of them related to oil, natural gas and chemical production—are signed and expected to begin in the next three years, according to the state’s economic development secretary, Stephen Moret.

The storm-recovery effort is a big reason why Louisiana has outpaced the rest of the country in job growth. The state’s overall number of nonfarm jobs increased 10.5% between October 2005 and April 2012, compared with a 1% decline nationally, according to government data analyzed by Moody’s Analytics.

Many of the best performers were areas such as construction, transportation, retail and leisure—sectors that are associated with the rebuilding and tourism rebound following Katrina.

The state’s population has also changed in the post-Katrina exodus, driving many of the poorest out at the same time that more-educated residents moved in. New Orleans lost more than 29% of its population from 2000 to 2010, but the people who now live in the city have higher education levels. In 2010, 33.2% of residents 25 and over in the city had a bachelor’s degree or higher, 5.1 percentage points above the national average, according to census data. That was up from 25.7%—just 1.4 percentage points above the U.S. average—in 2000.

Between 2005 and 2010 Louisiana saw an average net loss of 18,360 people a year who were over 15 and had income—and about half of them made less than $15,000 a year, according to an analysis of census data by Troy Blanchard, a demographer at Louisiana State University.

Still, the new tech jobs show the Louisiana economy’s diversification as neighboring states continue to struggle after the nationwide recession.

The U.S. Department of Commerce’s Bureau of Economic Analysis ranked Louisiana 28th in personal income per capita in 2010 and 2011, a significant improvement from the pre-Katrina years, when it ranked in the low- to mid-40s. It was 44th in 2004.

Louisiana’s unemployment rate was 7.1% in April, while the national average was 8.2%, according to the U.S. Bureau of Labor Statistics. Parts of the state had unemployment rates at or close to 5%.

When Mr. Schultz started traveling the country seeking seed money and workers for Louisiana tech businesses a few years ago, many people he met adopted a patronizing “pat-you-on-the-head” attitude, he says, as if Louisiana were one of the nation’s perpetual economic basket cases. But these days, he is getting serious interest. “Katrina is past,” he said.

Just across the hall from Launch Pad, iSeatz, a global provider of customized online travel software, has a large office full of coders.

“WE’RE HIRING,” its website announces in a red banner.

Asked what he would do if his start-up flops, Mr. Conrad shrugged and smiled, saying he has had multiple job offers in Louisiana, a drastic change from when he graduated. “You probably could have reasonably called me insane in 2002 for thinking I could stay in New Orleans and find a tech job,” he said. “Post-Katrina, there has been a massive change in attitude.”