On Thursday, the team announced via an official statement that Chilton would not race at Spa-Francorchamps, as they looked to resolve "contractual issues".
Chilton also released a statement, through his management company, revealing that he had volunteered to step down for the weekend's race "to allow the team to attract much needed funds by selling his seat".
Reserve driver Rossi competed in Friday's opening practice session, recording the 20th-fastest time, but during the action it emerged that Marussia had gone back on their earlier decision, with Chilton to regain his seat in the car for the remainder of the weekend.
"I can't go into too much detail on the individual instances but we are running an F1 team here," Marussia chief executive Graeme Lowdon told the BBC.
"There are a large number of commercial agreements that are involved and sometimes it just happens we reach a stage where for contractual reasons it's not appropriate for a driver to be in the car and we took that action.
"These things happen. It's the drivers' jobs to be flexible. Both Max and Alex are professional drivers who will take this in their stride.
"This is just a reflection of how the industry has to work sometimes."