The in-form Walcott is back in top form after some very bad luck with injuries and played a key role as Arsenal thrashed Aston Villa 4-0 in the FA Cup final.
Walcott followed up his hat-trick against West Brom last week by scoring the crucial opening goal at Wembley, rifling a shot home just before half-time.
The Gunners went on to score three more times in the second half and Walcott says they are now ready to seriously contend for Premier League glory.
“This team is blessed, and we have a fantastic squad,” he said.
“I have been at Arsenal for a long time and this is truly the best squad I have worked with, and I believe we could go and challenge next year.
“That is the ultimate goal. The FA Cup is fantastic and to win it in consecutive years, not many teams have done that, so it just shows how good this team actually is. The manager (Arsene Wenger) has had so much belief in us since day one.”
Walcott has yet to commit his long-term future to Arsenal but talks over a contract extension are due to resume in the summer.
For now, the 26-year-old is just happy to be contributing again, having recently been out for more than a year due to a serious knee injury which forced him to miss the 2014 World Cup.
“I have worked really hard and the manager has shown his faith in me, so I just wanted to repay him and the fans for their support,” said Walcott.
“I missed (the final) last season through injury and personal reasons, so it was nice to come back with a bounce in a winning team.”
Walcott’s season is not over yet because he is to link up with the England squad ahead of the June 7 international against the Republic of Ireland in Dublin and the Euro 2016 qualifier in Slovenia (June 14).
“England is always important,” said Walcott.
“Representing your country is a massive honour, so we will have some good times tonight and then, when it comes to meeting up with England, I will be completely focused ahead of the friendly and then the qualifier.”