Rossi, 22, has been a reserve driver at Caterham since 2012, and is also one of the team's primary simulator drivers.
While Montreal will represent his first Grand Prix action of 2014, he has previously completed numerous FP1 and test runs, including driving in the same sessions last year. He was 20th fastest in Canada and then 19th in the US, just over seven-tenths of a second slower than the Red Bull of four-time world champion Sebastian Vettel.
Rossi, who is also competing for Caterham's junior team in GP2, said: "Each time I step into F1 machinery there is an important job to do. Montreal and Austin are important races for me and I want to thank Caterham for the opportunity to continue my development to a full time race seat in F1.
"My GP2 program combined with my F1 team reserve driver duties give me invaluable insight and experience for my future. I've built up a lot of hours in the F1 simulator already this year, but Montreal will be my first visit behind the wheel of the CT05 on track.
"I look forward to a positive run plan for both the Canadian and USA sessions."
Caterham F1 team principal Cyril Abiteboul added: "Alexander will be continuing his development with two more FP1 sessions for us in Canada and the USA.
"While his focus this year is firmly on GP2 we are pleased to give him more opportunities to play an active role in the F1 team's race weekends and to have him help us develop our car at two races that are very important for us, both in terms of our season overall and with the strong support we have commercially in the North American continent."