Both titles claim officials have been burying weekly reports by the White House Coronavirus Task Force, which make recommendations on how to slow the spread of the infection.
“The state has given us no explanation as to why this crucial health information should be withheld,” said Julie Anderson, editor-in-chief of both outlets.
“We had no choice but to ask a court to intervene to uphold the public records law.”
The Orlando Sentinel began requesting the weekly reports in October. The governor's office provided three briefings after the newspaper got its lawyers involved.
However, DeSantis's office has not provided any reports from November, despite the outlet's repeated requests, according to the lawsuit.
It recommended that Florida make mask wearing mandatory, introduce stricter social distancing guidelines and limit the capacity of indoor and outdoor gatherings.
The report also urged leaders to begin warning about the risks of gathering during the December holiday season.
"Florida has seen stability in new cases, an increase in test positivity, and increasing hospitalizations and deaths, indicating unrelenting community spread and inadequate mitigation,” the report said.
Mr DeSantis, who has been tipped as a future Republican Party presidential candidate, previously ruled out tighter coronavirus rules.
“No one’s losing their job because of a government dictate. Nobody’s losing their livelihood or their business,” he said earlier this month at an elementary school in Kissimmee.
The Independent has contacted Mr DeSantis's office for comment.
The lawsuits were filed in a state court in Tallahassee in the same week that police raided the home of a coronavirus whistleblower amid a "cybercrime probe".
Rebekah Jones, a data scientist who helped design Florida's coronavirus dashboard, was sacked from her department of health job earlier this year for "insubordination".
She claims she was asked to massage Florida’s bleak coronavirus figures.
Since then, she has personally accused Mr DeSantis of covering up the reality of the outbreak in Florida.
Florida Department of Law Enforcement (FDLE) executed a warrant on Ms Jones's Tallahassee home on 7 December.
The FDLE said it is investigating whether Ms Jones accessed a government messaging system without authorisation to urge her former colleagues to speak out against the state's alleged suppression of coronavirus data.
State investigators said they traced the message, sent on 10 November, to an IP address connected to Ms Jones's house.
Ms Jones denies that she accessed the system improperly and says she lost access to her government accounts when she left her post in May.
She was not arrested or charged with a crime. A gofundme page set up to help fund her legal fees has so far raised $240,000.
Additional reporting by Associated Press
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