The team blamed "contractual issues" on the late change in plans. Rossi will be the first American to race in F1 since Scott Speed in 2007.
“Although it was not our intention to offer Alexander the possibility to race this season, in light of the circumstances we are pleased to be providing him with the opportunity to make his Grand Prix debut at this weekend’s Belgian Grand Prix in Spa-Franchorchamps," said team boss John Booth.
"Naturally we hope to resume normal service with respect to our established race driver line-up as soon as possible, but for now we wish Alexander well for the weekend ahead and we look forward to seeing him in action.”
“It goes without saying that I am thrilled to be given the opportunity to race in Formula 1 for the first time and I cannot thank the Marussia F1 Team for the faith they are demonstrating in me," said Rossi.
"It’s a very big moment for me and there’s a lot to prepare in a short space of time, but on the other hand I have felt ready for this for quite a while now.
"It is also exciting to be given this opportunity at such a fantastic and historical circuit as Spa-Francorchamps. I can’t wait to drive the MR03 from tomorrow and I hope to reward the team with a solid race weekend."