The Connacht tighthead was withdrawn 10 minutes after coming on as a half-time replacement in Saturday’s 59-16 victory over Tonga.
All 33 members of Andy Farrell’s squad trained on Tuesday ahead of the World Cup showdown with the Springboks in Paris.
Speaking of Bealham, Ireland scrum coach John Fogarty said: “He was obviously taken off the field at the weekend and failed his (head injury assessment).
“He’s subsequently passed his tests and he’s perfect, he was in a scrum today and he’s good to go, symptom-free.
“Our medics and World Rugby have cleared him fit to play so we’re delighted to have a full (clean) bill of health.”
Jack Conan and Dan Sheehan also took part in the session at Ireland’s base in Tours, potentially boosting head coach Farrell’s options for Saturday evening at Stade de France.
Number eight Conan has been sidelined since August 5 when he sustained a foot injury during his country’s win over Italy.
“Jack is doing bits and pieces today, he didn’t do a full-blooded one but he’s on the field and he’s going to do a little bit more tomorrow,” said Fogarty.
“He’ll be managed as a returning player would be but yeah, we’ve a full bill of health.
“Jack (will) do more tomorrow and it’s then a decision to see how he is. He’s up for selection, we’re on our feet, it’s been brilliant.”
First-choice hooker Sheehan sprained foot ligaments a month ago in the warm-up win over England.
“I saw him in a scrum today, so I was very excited to see him in scrums,” Fogarty said of the 25-year-old.
“We did some timing in our scrums, some drop-ins, and Dan took part.
“It’s great to see him back involved. He’s a player who’s returning so we’ll do a bit more tomorrow and see how he is.”
Ireland lead the way in Pool B following back-to-back bonus-point wins over Romania and Tonga and could seal progression to the quarter-finals by denting the Springboks’ title defence.
“There’s definitely an edge (in the camp),” said Fogarty.
“It’s an incredibly exciting week to be involved in. Everyone wants to be in the starting 15 and make the matchday 23 so competition for places is right up there. To be playing the world champions in Paris is incredibly exciting.
“We are clear in our heads as a group what the plan is and who is going to carry out that plan.”