The matches are taking place in St Tiernach's Park, Clones, County Monaghan.
The senior final starts at 14:00 local time and the minor final starts at 12:00 local time.
A spokesperson said: "The majority  of the supporters traffic will be travelling via the A5 on to the  N2 travelling onwards to Clones  via  the  N52 through Monaghan Town.
"This amount of traffic is expected to generate some congestion as it passes through Monaghan town.
"An garda sÃ­ochÃ¡na (Irish police) is asking those travelling to Clones to give themselves  plenty of time to avoid being delayed for the start of the match at 2pm.
"There is also a country music festival on in Monaghan town over this weekend and there are traffic diversions in place from 18:00 onwards today, which may affect  home-bound traffic.
"Delays can be expected from Monaghan town to Clones due to the volume of traffic particularly when both games are over."
Police in Monaghan are warning of heavy traffic as the Ulster football finals get under way on Sunday.