Gibson was deputy secretary for just three months before his new role, but President Barack Obama already has laid out some priorities for him.
During Friday's news conference in which Obama announced Shinseki's resignation, he also addressed some qualities and priorities needed in the next VA secretary.
Pressure had been mounting for Shinseki to step down amid a scandal involving long waits for care at VA hospitals.
"At this stage, what I want is somebody at the VA who is not spending time outside of solving problems for the veterans," Obama said.
The President said he wants someone who will spend "every minute of every day" finding solutions to the problems at the troubled department.
Obama ran through a list of problems for the next VA chief to solve: Has the VA reached out to all the veterans who are waiting for care? Have they had appointments scheduled? Is the system being fixed? What new technology is needed?
"That's what I want somebody at the VA focused on," he said. "Not how are they getting second-guessed, and speculation about their futures and so forth."
Before coming to the VA, Gibson was chief executive at the USO.
A West Point graduate, Gibson was an infantry officer in the Army. His grandfather and father served in World War I and World War II, respectively.
Gibson also has experience in the private sector, having worked for more than 20 years in banking.
Obama said he met with Sloan and "made it clear that reforms should not wait."
"They need to proceed immediately," Obama said.
In his last acts as secretary, Shinseki on Friday announced the firings of those responsible for misconduct, including senior leaders at the Phoenix VA hospital, where some of the most egregious cases of alleged fraud may have occurred.
Gibson's immediate priority, the President said, is to ensure that all veterans who call for appointments get them in a timely manner.
"Those are things that don't require rocket science," Obama said. "It requires execution, it requires discipline, it requires focus. Those are things that Sloan (Gibson) has."
Long-term solutions will require a review of the VA's budget, and its needs for doctors and technology, he said.