The Middlesex seamer was left out of the initial 16-man squad after suffering bone stress in the early stages prior to the recent Pakistan series.
Finn’s recovery went well enough for him to play in England Lions’ last two Twenty20 matches against Pakistan in the United Arab Emirates, taking four wickets.
The 26-year-old will join England in Potchefstroom on Monday night, but is not being considered for Tuesday’s warm-up match against a South Africa Invitational XI.
Indeed, he may yet have to sit out the second tour match in Pietermaritzburg and the first Test on Boxing Day before he is deemed ready for action.
In the meantime Chris Jordan, Chris Woakes and Mark Footitt will vie for the third seamer’s role behind James Anderson and Stuart Broad.
Finn said: “I’ve been really pleased with the way things have gone with the Lions. I’ve bowled my overs and my foot has come through fine. I’m excited by the prospect of linking up with the team out in South Africa.”
Head coach Trevor Bayliss had been monitoring Finn’s progress having been impressed by his Test comeback during last summer’s Ashes win, but was circumspect about a possible call-up on arrival in South Africa.
“We’re planning for this tour without him but, if he proves his fitness in the UAE and we do decide to bring him out here, that will be an absolute bonus,” said Bayliss. “The signs are good but there are still one or two small hurdles for him to get over.
“If he can get through those small hurdles pain free and bowling well, I’d expect to see him here at some stage.”
England wicketkeeper Jonny Bairstow welcomed Finn’s return to the squad, insisting the 6ft 7in bowler would be an important asset in pace-friendly conditions.
“It’s fantastic news,” said Bairstow. “We were really disappointed with Finny getting injured in the UAE.
“He’s an integral part of our squad and to have him back and hopefully pushing for a place in the first or second Test is fantastic.
“He’s had a bit of a break and he’s raring to go after putting some performances in for the Lions out in Dubai.
“Finny, with his height and extra bounce and pace, will bring a different aspect to our pace attack.”