The 24-year-old last played for his country 12 months ago in a friendly defeat against Greece.
However, Meyler is now determined to work hard and add to his four international caps in the coming months.
"I was delighted when I heard who had got the job," he told the Hull Daily Mail.
"Martin's a fantastic manager and it's up to me to keep playing well with Hull and force my way into his squad. It's up to the players to prove they deserve to be in the squad.
"They're both strong characters but they understand football so well, it won't be a problem. They can bounce ideas off each other and it can only help the squad. It's incredible for Irish football."
Meyler made his senior debut for Ireland in September 2012.