Free agent Mohamed has signed a one-year deal with the League One side after impressing on trial in Tuesday's friendly defeat against Bristol City.
The 22-year-old had spent a month's trial at Wrexham and manager Brian Carey was set to offer him a deal.
"I have an eye for goal and want to develop my career here at Swindon," Mohamed told the Swindon website.
"I am really looking forward to the new season and want to start getting on the scoresheet and impress the Swindon fans."
Mohamed, from Cardiff, had scored three goals in four friendly games for Wrexham, including one against Blackburn Rovers on his debut.
But as the Dragons hesitated in offering him his first contract in professional football, Swindon boss Paul Sturrock invited him to play for the Robins.
So impressed was Sturrock with Mohamed's performance that he made a contract offered less than 24 hours later.
"I was very pleased. He showed good potential. He showed he knows how to play," said Sturrock.
Mohamed chose to leave Welsh Premier side Carmarthen Town in the summer, having scored two goals in May's 3-1 Welsh Cup final win over Afan Lido.
He notched 32 goals in 79 Welsh Premier games after making his debut for Cwmbran Town at the age of 18.
Mohamed moved to Llanelli two years later, but really made his mark at Carmarthen with 21 goals last season, enough for former Old Gold manager Mark Jones to recommend him to Wrexham boss Brian Carey.
BBC