Walcott joined Everton from Premier League rivals Arsenal in the January transfer window for a fee reported by The Mirror to be worth £20 million.
The 28-year-old, who can operate as a forward or as a winger, has made a strong start to life at Goodison Park, scoring two goals and providing one assist in two Premier League appearances for the Toffees so far.
Everton manager Allardyce has stated that the England international did a lot of the negotiation himself to leave the Gunners for the Merseyside outfit.
Allardyce told The Mirror: “I think a lot of negotiation was done by Theo. Because of his service to the club and the fact he would accept what Arsene was doing — he is not a troublesome player who would throw the toys out of the pram — that respect between him and the club resulted in the move.
“He could have gone back to his hometown club Southampton, who were our big rivals, but the challenge he sees at Everton – can he get Everton to where they want to be? - he would help in that.
“There are no easy negotiations with Arsenal, believe you me, but eventually the insistence for the first time ever from Theo that he wanted to leave, plus the respect they have for each other and the service he gave, probably was a factor.”
Walcott is a good attacking footballer with a lot of pace, and the 28-year-old could prove to be a good long-term signing for Everton.
The former Southampton star had failed to progress at Arsenal, and it made sense for the North London outfit to sell him for (a reported) £20m in the January transfer window.
The Englishman is also going to play regularly for Everton, meaning that he benefits from the move as well.