Aston Villa have agreed a deal which will see "significant investment" be put into the financially-stricken club "immediately".
Egyptian Sawiris is estimated to be worth $6.8bn (£5.2bn), while American financier Edens owns the Milwaukee Bucks NBA franchise.
The deal - which has already been ratified by the EFL - will see Dr Tony Xia become co-chairman of the club and remain on the board, with the new investors detailing their plans to strengthen the Villa squad ahead of the new Championship season.
"I am extremely pleased to have formed a strategic partnership with Nassef and Wes. We have a common goal of delivering future success for Aston Villa and I look forward to working together to achieve this aim," Xia said in a statement on the club's official website.
"To have come so close to achieving promotion last season was a humbling experience. In finding such strong partners as Nassef and Wes we're gearing up to fight again and bring back the success that this club deserves and we all so want to provide it with. The future is exciting on a number of fronts and I look forward to exploring further business collaborations."
Sawiris and Edens added: "As lifelong football fans, we are excited and privileged to have become part of this great club. We believe that together we bring business and sports experience that will help strengthen the club to ensure Aston Villa can return to its rightful place in the upper echelons of English football.
"Our goal is to bring sustainable success to the club, building on its rich history while respecting its loyal fan base and unique culture. We understand that we are stewards of Aston Villa on behalf of the fans and we take that responsibility seriously.
"We look forward to working with Dr Tony to undertake a thorough assessment and evaluation of the club in the coming weeks and our priority is to strengthen the squads and structures ahead of the upcoming season and beyond."
Villa's first game of the new Championship season will come against Hull City on Monday, August 6.