In a statement, the Spanish side said the 29-year-old has been medically assessed and passed fit after his illness days earlier.
“Iñaki Williams has been assessed by Athletic Club's medical services, who confirmed the striker has now adequately recovered from an illness he's had over the last few days,” the club said.
“Iñaki will travel to Ghana early on Thursday morning to join the Blackstars' training camp ahead of their Africa Cup of Nations campaign.”
This comes after Athletic Bilbao revealed on Tuesday that Williams had an illness which required that he had enough rest.
The Basque club said the player had received treatment and was expected to be assessed again on Wednesday, adding that it had informed the Ghana FA of proceedings.
“Athletic Club player Iñaki Williams was assessed by the club's medical services early on Tuesday morning at Lezama as he has come down with an illness which requires him to rest,” the club said on Tuesday.
“Iñaki has received treatment and will be assessed again on Wednesday morning so that he can travel and join the Ghana training camp as soon as possible.
“The Ghanaian Football Association's medical team have been informed of the condition of the player.”
Meanwhile, the Black Stars have begun camping in Kumasi ahead of the AFCON, with 24 players partaking in training on Tuesday.
Chris Hughton’s side is paired in the same group with Egypt, Mozambique and Cape Verde and will be aiming to end a four-decade trophy drought in the Ivory Coast.