As the Fine Gael TD bids farewell to 12 months of personal and professional controversies, including a massive department overspend that cost the state 360 million euro in a supplementary budget, Mr Kenny said he plans to work closely with his right-hand man.
The department needs to be stronger, the Taoiseach said, but he believes Dr Reilly is the man for the job.
"It is a department that I intend to work with the minister more closely in 2013 to see that the objectives and the targets set out there are actually achieved," Mr Kenny said.
Dr Reilly has come under constant attack throughout the year following a series of controversies. Opposition parties have called for his resignation with both Fianna Fail and Sinn Fein tabling a motion of no confidence.
But the Taoiseach insists it takes time for all new ministers to get "a real handle" on their job and responsibilities.
Dr Reilly has been in the role for nearly two years.
Mr Kenny, who has defended the Health Minister in the face of harsh criticism, said that his was a particularly difficult ministry given the reforms required. Its complex structure, consisting of health boards "squashed together" and the Health Service Executive on top of that, make it more challenging.
"And given the fact it concerns at some stage or other, every single person in the country, I think the fact that the changing of that structure by Minister Reilly obviously is work that is serious and is ongoing here," he said.
He said he believes "very strongly" in Dr Reilly and that he will lead the health reforms, delivering effective frontline services with fewer numbers and less resources.