The England international has struggled with serious injuries in the past two seasons and was limited to just 15 Premier League starts since the beginning of the 2015-16 campaign.
He is now fully fit and he scored his first league brace since playing for Manchester United in 2013, as well as laying on an assist for Alexandre Lacazette, in a straightforward 3-0 win over the Cherries.
Welbeck's second goal was praised by manager Arsene Wenger and Welbeck reckons his preparations have allowed him to hit the ground running this year.
"The past two years I didn't have a pre-season and that made it a bit difficult for me," he said.
"I'm pleased to have a pre-season
With some of the games that we've played at the start of the season it's not gone too well, but I'm pleased to be on the scoresheet and long may it continue.
"The second goal is one that, once you've been hitting those repetitions in training, it becomes a lot easier for you to do
I got into that position and I didn't think twice about it."
Welbeck's brace inspired the Gunners to a much-needed victory following two successive defeats heading into the international break - including a 4-0 loss at Liverpool.
Bournemouth offered very little at the Emirates Stadium having pushed Manchester City all the way last time out.
Manager Eddie Howe was unhappy with the display and, with Bournemouth still without a point so far this season, midfielder Dan Gosling wants a reaction against Brighton on Friday night.
"We need to bounce back," he told the club's official website.
"Brighton's coming up to a must-win game at the moment, we need to get our season up and running now with this home game.
"The boys were unlucky against Man City, but we can't keep saying that because against Arsenal we were nowhere near it
Next week every single man has to be better, stand up and be counted."
Source : PA