The Chile international, 25, completed a move to the Emirates Stadium from Barcelona last week for around £30m.
"Sanchez is a world-class player and I enjoyed watching him play for Barcelona and for Chile at the World Cup," Walcott told Arsenal's official website.
"He's still very young as well and he is going to show so much pace and power, which we lacked a bit last year.
"With me and him on the flanks, a lot of teams won't be looking forward to playing Arsenal this year."
Arsenal begin their Premier League campaign at home to Crystal Palace on August 16.