D'Ambrosio has been a test driver for Lotus since leaving Marussia in 2011 and will now have the chance to race for the team who currently stand third in the constructors' championship.
Team principal Eric Boullier said: "When we signed Jerome as our third driver we signed a man who is highly motivated, fresh, talented and who contested the full 2011 season.
"We hope that this will pay dividends when he drives the car this weekend in Monza. We know that Jerome is well integrated into the team and that he did a good job when he drove the E20 at the Mugello test.
"Now he has the challenge of a grand prix at the challenging circuit of Monza, in a car which is capable of finishing on the podium."
Grosjean has accumulated 76 points so far this season and sits in eighth place in the drivers' standings.