DOVER — Gov.-elect John Carney on Tuesday nominated four candidates for cabinet positions, two of whom already hold the offices.

In addition to selecting Jeff Bullock and Jennifer Cohan to continue their roles running the State and Transportation departments, respectively, he also nominated Perry Phelps to head the Department of Correction and Mike Jackson to lead the Office of Management and Budget.

Mr. Jackson currently serves as deputy controller general and previously worked for the University of Delaware, the Delaware Department of Education and OMB. The office is responsible for crafting the state budget, managing human resources across state government and handling the state’s pension investments.

He will succeed Brian Maxwell, who has been in the position for less than a year and is going to work for New Castle County.

“Mike has the experience and leadership skills necessary to help us immediately confront the budget challenges we face as a state,” Gov.-elect Carney said in a statement. “I’m confident that Mike will help us responsibly balance our budget, protect taxpayer dollars and make smart investments that will help all Delawareans thrive.”

Mr. Phelps, the deputy commissioner of correction for the past two years, will lead the correctional system, replacing Robert Coupe.

He previously was bureau chief of prisons, warden of James T. Vaughn Correctional Center and an administrator with the Department of Services for Children, Youth and their Families.

“Perry is well-respected inside and outside of the Department of Correction, and nobody is more prepared to lead the department,” Gov.-elect Carney said. “He will offer a unique perspective on the issues facing Delaware’s criminal justice system, and I’m thrilled he has agreed to join the team.”

Ms. Cohan, who has been the secretary of transportation since January 2015, will continue in her post. Before becoming DelDOT secretary, she was the director of the Division of Motor Vehicles and had held other positions with the Department of Natural Resources and Environmental Control, Controller General and DelDOT.

“Jen has a proven record at DelDOT that will be a significant asset to our administration and to the people of Delaware,” Gov.-elect Carney said.

“During her time at DelDOT, she has helped modernize the DMV and successfully advocated for new investments in Delaware’s transportation

infrastructure. Her leadership will help us make even more progress.”

Mr. Bullock, who has worked for past governors and New Castle County, was one of the original cabinet secretaries under Gov. Jack Markell, taking over the agency in January 2009.

The Department of State oversees 18 different divisions, including Arts, Corporations, and Historic and Cultural Affairs.

“Jeff and I worked together in the (Tom) Carper administration and he shares my belief that government should expand opportunities for all Delawareans to succeed,” Gov.-elect Carney said. “His public service experience at the federal, state and local levels provides a unique perspective that allows him to take on wide ranging challenges from protecting our lucrative corporate franchise to leading our efforts to expand the port. He will be an important part of our team as we address the state’s financial challenges next year.”

The nominations must be approved by the Senate next month. Gov.-elect Carney will be sworn in Jan. 17.