The striker was a doubt after being withdrawn after an hour of Chelsea’s friendly win over Barcelona in Washington on Wednesday after feeling a twinge in his hamstring.
Cahill, meanwhile, was also replaced after a clash of heads while scoring a late equaliser as the game finished 2-2 with Chelsea prevailing 4-2 on penalties.
However, Mourinho has now confirmed that both men are fit to face the Gunners and that he has no injury concerns ahead of the start of the new season.
"All good,” he told reporters."'There are no concerns, no protections [for Costa]. We have three top strikers. I'm not worried. No problem."
The Chelsea boss also offered his view on the news that Premier League fixtures would not be adjusted to help teams in the Champions League.
"My reaction is that here we have four teams in the Champions League and we will not make a big noise of it," he added.
"But one day when England has only three teams in the Champions League people will wake up."
