Rufai's journey to Elfsborg saw him make the transition from Ghana Division Two League outfit, Inter Allies Football Club.
The club expressed their excitement over the acquisition, stating, "IF Elfsborg are thrilled to announce the signing of Ghanaian center-back Rufai Mohammed from Inter Allies FC. Rufai has inked a deal that extends through the 2028 season."
Rufai expressed his delight about completing the move which serves as the next step in his career.
"I am very happy to be here. The people I have met in and around the team are amazing and very helpful," said the youngster.
"I am tall, strong and like to take a place in the back line. I always work hard because I demand a lot from myself and constantly want to develop and get better.
"I look positively at the future and look forward to the chance to fight and contribute good things for the team and the association. I just want to get started for real now."