Sanchez netted 25 times in his debut season for the Gunners but had drawn a blank in eight games this term before hitting top form in the north Londoners’ 5-2 win at the King Power Stadium.
“I am sure he is going to flourish now with many, many more important goals,” said Walcott.
“It has been a long time coming, he knows that himself, but he is very pleased. He is a top quality player and even when he is not scoring goals he works so hard for us. He tracks back and does a lot for the team.”
Walcott revelled in another start at centre-forward and capped a widely-praised performance with his fifth goal in six games for club and country.
“I have always said I want to play up front,” he added. “When I get the opportunity I can improve and learn the position a little more. The manager has had faith in me and I just want to repay him.”
Victory over high-flying Leicester lifted Arsenal into the Premier League’s top four, three points behind new leaders Manchester United, who visit Emirates Stadium in a top-of-the-table clash on Sunday.