Rovers, who have lost Josh King and Tom Cairney in recent weeks, are under a transfer embargo so are unable to pay for players but 23-year-old Frenchman Petshi has penned a 12-month deal, with the option of another year, after playing for Bastia last season.
He was taken on Blackburn’s recent pre-season trip to Portugal and played in the friendly against Accrington earlier this month.
“I’m very happy to sign for Blackburn,” Petshi told the club’s official website.
“It is a good club, with good facilities and a good team.
“It has always been my goal to play in England. I love English football and I think my physique will suit the English game.
“I’m here to play, to learn and to help the team win lots of games.”
Koita, 24, began his career at Montpellier and recently played for Caen, scoring seven times in a two-year spell there.
“I’m very happy to be here, it is my dream to play in England and now my dream has come true,” he told Blackburn’s official website after agreeing terms on a two-year contract.
“I want to work hard and I hope I win many games for my new team. In France the game is more technical, but here it is physical, it is very strong. I am here to learn and to do my best.
“I am really excited because I have waited to be here and now I am, I want to be happy.”