"Wayne has been an excellent captain for England and the manner in which he has fulfilled the role made it an easy decision for me to ask him to continue," Allardyce told the FA website (www.thefa.com) on Monday.
Rooney, 30, took over as captain from Steven Gerrard in 2014 and is on course to become England's most-capped outfield player.
If he plays in the World Cup qualifier against Slovakia on Sunday, the forward will be making his 116th international appearance, overtaking David Beckham.
Only former goalkeeper Peter Shilton (125) won more England caps.
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"Wayne's record speaks for itself," said Allardyce who took over last month after England crashed out of the European Championship in the round of 16. "He is the most senior member of the squad and is hugely respected by his peers.
"All of these factors point towards him being the right choice to lead the team."
Rooney said earlier this month that he would make himself available for England through to the 2018 World Cup in Russia and would then decide on his international future.
(Writing by Clare Fallon; Editing by Tony Jimenez)
