The England international moved to Goodison Park last month in a £20million deal, having found opportunities limited this season under Gunners boss Arsene Wenger, making just six substitute appearances in the Premier League.
By contrast, Walcott has played the full 90 minutes twice since joining Everton, providing an assist in his first match and scoring twice in Wednesday's win over Leicester.
And Allardyce expects the 28-year-old to play an increasingly important part over the coming seasons.
"He'll be doing the team talk tomorrow," joked Allardyce ahead of the trip to north London. I think he is looking forward to it. I am sure he will get a good reception when he goes back to the Emirates, considering the time he spent there.
"Everyone can understand why he has left because now he has the opportunity to be one of the key players for Everton.
"I think he saw that was going to be the case (for Arsenal) last season when he played 30-plus games and scored 19 goals.
"Then all of a sudden this season that hasn't been the case but he can be a pivotal figure for us in the future. Hopefully he can go and perform as well as he did on Wednesday night."