Frenchman Grosjean was banned for one race after causing a pile-up and smashing into championship leader Fernando Alonso's Ferrari at the first corner of last Sunday's Belgian Grand Prix at Spa-Francorchamps.
D'Ambrosio, who is of Italian extraction and raced for Virgin (now Marussia) last season without scoring a point, is the team's official reserve and will partner 2007 world champion Kimi Raikkonen at Monza, Lotus said in a statement on Tuesday.
"My desire for 2012 has always been to get back into the seat of a Formula One car, so I am grabbing this opportunity with both hands," said D'Ambrosio.
"I want to reward the faith that the team has in me with a good haul of points from the race."
The last Belgian to finish in the points was Thierry Boutsen, who came fifth for Ligier at the Australian Grand Prix in Adelaide in November 1992.
There are no Belgian or Italian drivers in the championship this season.
Lotus have a quick and reliable car and are ahead of Ferrari, who can count on most of the support at Monza, in third place in the constructors' standings.
Raikkonen is a title contender, despite not yet having won a race in his comeback season, with four podium finishes in his last five starts and six this season in total. Grosjean has also had three top three placings.
Monza, the quickest circuit on the calendar and Ferrari's backyard, is the last race of the season in Europe and d'Ambrosio recognised it would be a "massive" challenge.
Last year his car broke down on the warm-up lap, and he has not raced on the circuit since he was in the GP2 support series, when he finished on the podium.
"It will be challenging but I am already part of the team, I know everyone and I will have great support from them to do the best I can," he said.
"I will be focused 100 percent to make full use of free practice because that could be the key for me this weekend."
Team principal Eric Boullier said d'Ambrosio deserved his chance.
"The car he'll be driving should be able to fight for the podium, and he won't have much track time to get ready. That's a challenge and I'm sure that Mr d'Ambrosio can surprise a few people," he said.