The Briton, who normally races in GP3 for Carlin, takes the place of Sean Gelael, who is concentrating on his full-time Formula Renault 3.5 programme at Silverstone instead.
A race winner in his rookie season in GP3 last year, the 23-year-old's second campaign began with a podium in Barcelona, but he has not scored points since the third race of the year at the Red Bull Ring.
"I'm extremely excited to drive a GP2 car for the first time," said Mardenborough.
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"It's an opportunity that I couldn't turn down.
"I want to move up to GP2 in the future so to have this experience now is very valuable.
"I want to be competitive but the challenges in GP2 are very different to GP3; with DRS and two tyre compounds, as well as longer races and pit stops, although I'm used to those from sports car racing.
"It's going to be a big step up but I'm going to give it everything."
Team boss Trevor Carlin said he was pleased to hand the Monza vacancy to another of his existing drivers.
"With Sean busy completing his full season in Formula Renault 3.5, we had the ideal opportunity to give a driver a taste of GP2 at one of the greatest circuits in Europe," said Carlin.
"Jann is a very talented and fast driver and has suffered some bad luck this season which means he hasn't claimed the results he's capable of.
"Although this weekend will be a big learning curve for him, we're pleased to give one of our GP3 drivers the opportunity to step up to the next level and will be focused on helping Jann get the most from the experience."
Carlin has confirmed that Mardenborough's GP3 seat will be left vacant for this weekend.
Another GP3 racer, Patric Niederhauser will also make his GP2 debut at Monza, with Lazarus replacing Nathanael Berthon.
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