After Wales lost yet another back to injury last week when winger Liam Williams was ruled out of the tournament, coach Warren Gatland has shown faith in Morgan, switching George North back to his preferred position on the left wing.
Morgan made his debut in the August warm-up victory over Ireland and also played in the World Cup win over Fiji and his club boss said he expected him to revel in the occasion.
"Nothing fazes him," Dragons director of rugby Lyn Jones told Wales on Line.
"The bigger the challenge, the better he plays. He has huge respect for his opponents, but at the same time he wants to get one over on them and he goes full out to win that little individual battle.
"Because of his age he wants to go and play hard and have a go."
Gareth Anscombe retains the fullback slot and will also win his third cap.
In two other changes to the side beaten by Australia, Jenkins returns in the front row for his 18th World Cup appearance, with Dan Lydiate back as blindside flanker, allowing captain Sam Warburton to return to the number seven position.
Luke Charteris and Alun Wyn Jones continue in the second row with Wyn Jones making his 100th international appearance, this being his 94th Welsh cap after six games for the British and Irish Lions.
"After coming through an incredibly tough pool we are excited to be in the quarter-finals and returning to Twickenham," Gatland said in a statement.
"The physicality and intensity of the matches so far will stand us in good stead for what is going to be a huge battle against the Springboks.
"They have grown game on game in this tournament and we know the challenge that faces us from a talented South African side."
Wales won the last meeting of the teams, 12-6 in Cardiff in November 2014, ending a 16-match losing streak that began in 2000.
Their only previous World Cup meeting was in 2011 when the Springboks edged a closely-fought game 17-16.
Wales team:
Team: 1-Gethin Jenkins, 2-Scott Baldwin, 3-Samson Lee, 4-Luke Charteris, 5-Alun Wyn Jones, 6-Dan Lydiate, 7-Sam Warburton (captain), 8-Taulupe Faletau; 9-Gareth Davies, 10-Dan Biggar, 11-George North, 12-Jamie Roberts, 13-Tyler Morgan, 14-Alex Cuthbert 15-Gareth Anscombe.
Replacements: 16-Ken Owens, 17-Paul James, 18-Tomas Francis, 19-Bradley Davies, 20-Justin Tipuric, 21-Lloyd Williams, 22-Rhys Priestland, 23-James Hook.
(Editing by Julian Linden)
