Marwa Kenawy, who started a hunger strike on March 31 to pressure authorities into arresting them, said both men will now start serving a seven-year jail term handed to them in absentia in May 2018 over the incident.
However, they will now have a chance to lodge an appeal.
"I got a confirmation that they turned themselves in today after receiving numerous calls and messages telling me that they had appeared [at the police station]," Kenawy told ABC.
The 45-year-old ended her hunger strike on Monday after a criminal court upheld the seven-year sentences against the suspects for involuntary manslaughter and possession of firearms, but insisted she "had not given up."
With one of the culprits being a police officer and the other the son of a late member of parliament, Kenawy was worried they were being protected by their connections.
"I have never got an explanation from any officials over why the two men had not been arrested," Kenawy, dressed in the traditional all-black of mourning, told ABC News in an interview last week. "But for me, it's obvious [they are being protected], there are no other reasons,"
"I decided to resort to the hunger-striking option until they are arrested because all my other efforts were in vain. I went through all the possible channels before starting the hunger strike."
Celebratory gunfire is a common practice at weddings in southern Egypt and rural parts of the country, but has now spread to more urban areas such as the capital.
Kenawy said that while she is striving to bring justice to her son, she also has her eyes set on the bigger picture.
"Youssef's death is a message from God, everything happens for a reason. He was a victim and I'm required to bring his right and the rights of many other people," she added.
"There are many similar incidents which are not getting the same attention. I have a role to raise awareness and call for the rule of law, so that many people could be deterred."