Max Chilton (GBR) Marussia F1 Team MR03. Formula One World Championship, Rd11, Hungarian Grand Prix, Race Day, Hungaroring, Hungary. Sunday, 27 July 2014. © Sutton Images
The team said Chilton, who has raced for the Banbury-based squad since 2013, was being substituted "while contractual issues are resolved".
Rossi, 22, only joined Marussia as test and reserve driver last month having previously served in a similar role at Caterham, contesting four Friday practice sessions over the past three seasons.
"It goes without saying that I am thrilled to be given the opportunity to race in Formula One for the first time," Rossi said. "I cannot thank the Marussia F1 Team enough for the faith they are demonstrating in me.
"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."
Team principal John Booth admitted the driver change had not been planned, and said the team is hoping to resolve the situation as quickly as possible.
"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," Booth said.
"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."
Rossi will be the first American to compete in F1 racing since Scott Speed made his final appearance for Toro Rosso in Germany in 2007. He will also be the second debutant at Spa this weekend, following Caterham's decision to replace Kamui Kobayashi with three-time Le Mans winner Andre Lotterer.