Topeka — Kansas is moving forward with plans to have the nation’s largest private-prison operator build a new state prison after departing Republican Gov. Sam Brownback cut a political deal to win over wary GOP legislative leaders Wednesday.

The Legislature’s eight top leaders approved a plan to have Tennessee-based CoreCivic Inc. build a 2,432-bed prison near Kansas City to replace the state’s oldest and largest correctional facility there. The state would buy the new prison in Lansing over 20 years through a lease with the company, paying a total of $362 million.

The top lawmakers’ approval was required by a state law authorizing the project last year. The vote among the leaders was 5-3, the exact tally Brownback needed for the project to go forward. The final vote was delayed nearly three weeks because several Republican leaders wavered amid skepticism about whether the lease-purchase deal was the most cost-effective option.

Two of the Senate’s top three Republicans didn’t come aboard until Brownback’s office announced an hour before the meeting that it was dropping plans for an overhaul this year of the state’s Medicaid health coverage for the poor and disabled. GOP leaders had worried about the potential cost and said problems with the existing Medicaid program must be worked out first.

Brownback won the go-ahead for the prison project just before the U.S. Senate confirmed his appointment as U.S. ambassador-at-large for international religious freedom. Stopping the Medicaid overhaul saved him from a stinging political defeat on the prison project just before he steps down and Lt. Gov. Jeff Colyer is elevated to governor.

“That was a major, major decision point for me,” said Senate Majority Leader Jim Denning, an Overland Park Republican.

Lawmakers in both parties agreed that the Lansing prison has major problems. Parts of it date to the 1860s and feature long rows of tiered cells with bad sight lines, but even newer parts built in the 1980s were poorly designed.

“It just needs work,” Brownback said. “The place is crumbling down.”

The department has estimated that a new prison could be staffed with 46 percent fewer employees — saving the state enough money to cover annual lease payments. While CoreCivic would be responsible for maintenance, the state would oversee staffing and day-to-day operations.

Democratic leaders were skeptical of the projected staffing and cost savings, and questioned whether the project would be cheaper over time if the state issued bonds to finance it.

“We will rue the day, I believe,” said Senate Minority Leader Anthony Hensley, a Topeka Democrat.

CoreCivic CEO Damon Hininger said construction could begin in a few weeks. The company has had similar projects in California and Oklahoma and is pursuing one in Colorado. He said the Kansas project could be a model for others in states with badly aging prisons.

“There are other states, we know, around the country that are looking at Kansas and thinking about how we could duplicate this kind of solution,” Hininger said.