Walcott told Saturday's Official Arsenal Matchday Programme that his stomach for the battle is second to none.
"[They were] brilliant - really important goals as well," he said.
"The Newcastle win was massive and he showed that desire to get from defence to attack and latch onto things. He's an absolute soldier, someone you'd always want in front of you, a real leader who just wants to win.
"To see him banging in another big goal at Everton was great. I'm happy for him - he had his injury problems last season but he's one of the best defenders in the world without a doubt."