Meyler, 23, swapped Sunderland for the Tigers earlier this month when he signed a three-and-a-half-year deal after initially arriving on loan in November and he wants top-flight football next season.
"I want to be playing Premier League football in six months time, not three-and-a-half years," he told the club's official website.
"I'm looking at the next few months and the next 18 games and picking up enough points in those games to make sure that Hull City can be in the Premier League next season.
"That's the reason I signed and I believe that is the reason everybody is here because they believe that this club can be in the Premier League."
Meyler has turned in a string of impressive displays for Hull since teaming back up with former Sunderland boss Bruce and coaches Stephen Clemence and Keith Bertschin.
"I certainly think that's the reason the manager came here," the Republic of Ireland international added. "If he didn't believe that this club could be up there, he wouldn't be here.
"When I look back to when I came here on loan, signing permanently would have been a massive decision.
"But having played regularly here for two months and helped the team to win games, coming here permanently turned into a no-brainer."