Ramsey, on his first Premier League start since returning from injury, opened the scoring after 31 minutes when he fired past Steve Harper, before Podolski added a second with an emphatic finish just before the break.
The Germany international added his second of the afternoon - his fourth in two games - early on in the second half as Arsenal cruised to the three points at the KC Stadium.
Hull did hit the woodwork through Jake Livermore in the opening 45 minutes, but Wenger was satisfied with how his side controlled the game and avoided some early scares to seal the win.
"We kept a clean sheet, we scored three goals and overall, I believe that performance was good," he told Sky Sports.
"We were tested in the first half from a very physical game. We responded with great movement and scored.
"In the second half, we controlled and it was easier and overall, it's a convincing win.
"We looked dangerous to score goals again. We had a few away games where we looked toothless and to think our combination game and our speed in the game was back and they looked like scoring.
"In the Premier League, you're always a bit apprehensive before every game and you want your team to perform as well as you can and when your players are out, you have to cope with it."
Wenger also hailed the form of Podolski and remained insistent that he is most effective from out wide rather than his preferred role as a central striker
"I think so," said Wenger when asked if the left wing is Podolski's best position.
"He's popping up in the box at the right moment, it's more important for him to be consistent there. I think it suits him to have a physical player in front of him."
Hull appealed for a foul in the build-up to Arsenal's second goal as Mikel Arteta clipped Nikica Jelavic, but Wenger was not convinced.
"Honestly, I didn't feel it was a foul," he said. "If he had given it I would have not complained but it was 70 yards from the goal."
The two sides are set to meet again at Wembley in the FA Cup final next month, but Wenger was keen to concentrate on securing a top-four finish despite cruising to the win over Steve Bruce's men.
Winning their three remaining league fixtures will clinch Champions League football for the Gunners after capitalising on Everton's midweek loss to Crystal Palace.
"Premiership is Premiership. Every game is different. The Cup final will be different," he said.
"For us at the moment, we are completely focused on the Premiership to finish as strong as we can.
"It's in our hands to win our games so let's just focus on winning the games. We have a great desire to do it and I think we can, but it's down to the quality in the games."