Allardyce, 61, has signed an initial two-year contract after the FA agreed compensation with Sunderland.
Manchester United striker Rooney, England`s all-time leading goalscorer, was part of the squad knocked out of Euro 2016 by Iceland in June.
"He will probably bring a different way of playing to England," he said.
"Hopefully it`s a good way and we can be successful under him."
I can`t stop smiling because I`ve got this job - Sam Allardyce
The 30-year-old said he had no intention of retiring from international football.
"Am I going to carry on?" said Rooney, who has scored 53 times for England in 115 appearances. "It was asked of me after the Euros, but yes, I`ll be there."
The former Everton striker was speaking during United`s pre-season tour of China, which they started with a 4-1 defeat by Borussia Dortmund.
England captain Wayne Rooney welcomes new manager
24 July 2016
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England captain Wayne Rooney says the Football Association have made a "good appointment" by naming Sam Allardyce manager of the national side.
