A man has been arrested on suspicion of arson in connection with the fires.
Patients were "dragged outside" Royal Stoke University Hospital when fire broke out in the main building at about 18:00 BST on Wednesday.
An hour earlier, there was a blaze in toilets at Staffordshire University.
On Thursday, Staffordshire Fire and Rescue Service said the hospital fire was started deliberately, with Staffordshire Police later saying it was linking that incident to the university fire.
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A force spokesperson said a 39-year-old man had been arrested on suspicion of arson with intent to endanger life.
Disrupted hospital patients were returned to wards by 23:15 BST on Wednesday, according to University Hospitals of North Midlands NHS Trust which runs the site.
The A&E unit reopened on Thursday.
Deputy chief fire officer Rob Berber said: "The fact that this fire was deemed to be deliberate is very concerning and we are working closely with Staffordshire Police to aid in their investigation into this incident."
He said one man was treated for smoke inhalation at the scene.
No one was injured, police said, in the university fire which happened at about 16:45 BST on Wednesday in the Beacon building on College Road, Stoke-on-Trent.
The hospital trust said people should continue to attend outpatient appointments unless contacted directly.
On Wednesday, eyewitness Paul Bradbury, who had gone to the hospital to visit his mother, said people were "dragged outside in their beds and on mattresses" and "it was quite surreal to see".
A fire which forced patients to be evacuated from hospital while still in their beds is being treated as arson - and linked by police to a university blaze on the same day.