The courses could be taught only in counties where casinos are legal — some areas along the Mississippi River and the Gulf Coast and in places with casinos run by the Mississippi Band of Choctaw Indians.
Republican Gov. Phil Bryant did not immediately say whether he'll sign or veto the bill
"The governor will take it under consideration once he receives it," Bryant spokesman Mick Bullock said Thursday.
The House has passed similar bills for years, but they died in the Senate.
This year, the bill moved through the Senate first, passing 34-17 on Feb. 7. The bill cleared the House 78-37 on Thursday.
Overriding a veto takes a two-thirds majority in both chambers. There would be enough votes to override a veto, if no lawmakers change from support of the bill to opposition.
Some religious groups oppose any boost to gambling. Supporters say the change could let Mississippi residents prepare themselves for high-paid jobs.
Mississippi has had legally run casinos since 1992, but Rep. John Read, R-Gautier, said colleges or universities need legislative permission to offer courses such as casino management or slot machine maintenance.
Tulane, a private university based in Louisiana, has taught courses on the Mississippi Gulf Coast for several years, including casino management classes. The University of Southern Mississippi offers a bachelor's degree in casino and resort management, with courses taught on its Gulf Coast campus, according to the university's website.
"Southern Miss was the first university in the state of Mississippi officially designated by the state Institutes of Higher Learning to offer this major, and even today is one of very few with the program," the website says.
During House debate, Rep. Becky Currie, R-Brookhaven, asked Read whether colleges and universities need the Legislature's permission to offer casino courses. Read said they do, and he specified that schools would not be allowed to teach people how to play blackjack or other casino games.
Currie was skeptical about the motivation for trying to change the law and the political repercussions for legislators who support a change.
"Do you think this is kind of a way to blame this on us?" she asked.
Currie was one of five House members who did not vote for or against the bill.
Mississippi Gulf Coast Community College President Mary Graham welcomed the bill and said she hopes it will become law.
"We have plans to start working on it immediately and launch a program as soon as possible," Graham said Thursday at the Capitol.
Associated Press writer Jeff Amy contributed to this report.