That will include his home grand prix in Austin, Texas, on Oct. 25.
Merhi will return for the Russian Grand Prix in Sochi and Abu Dhabi season-ender because Rossi has GP2 commitments.
The American, currently second in that series behind runaway leader Stoffel Vandoorne of Belgium, will be the first U.S. driver on the Formula One grid since Scott Speed competed for Toro Rosso.
"I’ve been prepared for this opportunity for quite a while now," said Rossi, who nearly raced for Marussia in Belgium last year when the team threatened to drop Britain's Max Chilton in a contractual dispute.
"Many will know from 2014 that the team and I already have a strong relationship and there’s a bit of unfinished business for me here," he added.
"This is a small F1 team that has been through so much. They exemplify passion and true strength of character, and their comeback this season is extraordinary. I’m honoured to be part of this legacy and their continued growth and success."
Rossi took part in Friday first practise for the team in Spa last year but by the time he had stepped out of the car, the dispute with Chilton had been resolved.
Marussia then went into administration and missed the last three races of 2014, returning this season only after finding a buyer at the 11th hour.
Rossi had also been linked to the U.S.-based Haas Formula One team, who are to debut next year, but they recently poured cold water on his chances.
"Singapore is a circuit I really enjoy and the timing of my debut could not be more perfect. There’s a lot of work ahead and I’m looking forward to a busy end to the 2015 season," he said.
Manor principal John Booth said he was delighted to give Rossi his chance.
"He is widely-regarded as a driver who is on the cusp of an exciting F1 career and his current form in the GP2 Series has done much to reinforce his clear potential," he said.
(Reporting by Alan Baldwin, editing by Toby Davis)
