The 15-year-old boy turned himself into police on Sunday evening.
"He had seen television footage and though that perhaps that he was the one we were looking for," said Lars-Erik Baarsen at Södermalm's police.
The boy was interviewed during the evening and was later released on the advice of the prosecutor.
"They have had sex but he perceived it as consensual," said Tomas Järnkrok at Södermalm's police after hearing the boy's version of events.
The 19-year-old girl was at Eriksdalsbadet, the largest and most-visited of central Stockholm's swimming pools, with a friend. When she left the pool to go to the toilet she claims that she was raped by the boy.
The teenager was taken to Stockholm South General Hospital's rape clinic for care.