The 41 pupils and seven staff from Arthur Terry School, Sutton Coldfield, were kept "safe and well" and were with a British Embassy member, the school said.
The children were at Istanbul Ataturk airport where they were due to get a connecting flight to South Africa.
The school said the staff and children were now on their way to Cape Town.
A statement said the students were "delighted" to be carrying on with the trip, and were flying overnight on Sunday.
The Foreign Office has said that the situation in Turkey now "appears to be calming".
The children left for the Turkish Airlines flight on Friday morning for the two-week trip.
Head teachers Neil Warner and Richard Gill thanked parents for their "tremendous support".
A statement said: "It's great to know that many of you have had direct contact with your sons/daughters and know that they are safe, well cared for and in good spirits."
Andrew Mitchell, Conservative MP for Sutton Coldfield, has been speaking to the teachers, including one of the trip leaders, Sue Bailey.
He said it had been a "very scary and unpleasant experience" for the group.
"Parents were naturally extremely concerned," he said.
The school was able to quickly pass on information to re-assure them, he added.
Mr Mitchell said the children had been fed and been able to sleep at the airport.
Meanwhile, Turkish Airlines said "upon the call" of President Recep Tayyip Erdogan, its operations at Ataturk airport were "back to normal and flights have begun".
The senior school said earlier the students were accompanied by "seven outstanding and experienced members of staff", including the assistant head teacher.
One mother appealed on Twitter for the Foreign Office, Turkish Airlines and media outlets to "please get our children out of Ataturk airport".
In South Africa, the group are planning to drive to a outward bound centre in Sedgefield on the Western Cape, where they are due to take part in community projects, working in two schools.
Information about the trip said it would provide a "real insight into a totally different culture and way of life".  The students raised funds for their trip through events such as a fun run and raffle.
Turkey's PM Binali Yildirim said some 2,839 soldiers, including high-ranking officers, have been arrested over the attempted coup
More than 40 Birmingham pupils were stuck at an airport in Turkey as a result of an attempted military coup.