The 35-year-old Brown won a training camp competition over McManus, who was traded Tuesday by the Giants to the Broncos for a conditional seventh-round pick in the 2015 draft.
The 23-year-old McManus, a strong-legged rookie, will serve as a temporary replacement for suspended Pro Bowl kicker Matt Prater. The Broncos waived rookie kicker Mitch Ewald after announcing the trade.
"I think Brandon will kick in this league," Giants coach Tom Coughlin said Tuesday. "He's a very powerful young man. Needs a little bit of work on the finer kicks, but certainly he demonstrated his ability to kick it through the back of the end zone."
McManus looked good on kickoffs during the preseason, but Brown did nothing to lose the job with the Giants. He was 23-for-26 on field goal attempts for the Giants last year, including 8-for-10 on kicks of 40 yards or longer.
"It's never fun," Brown said of beating out McManus. "He was upset, and it just as easily could have been the other way. He's one of those guys, he's going to be a lifer. He's going to be a 10-year guy. He's got that kind of talent, and he's got that kind of head on his shoulders."
Prater has been suspended for the first four games of this season for violating the NFL's substance-abuse policy. Because of Denver's Week 4 bye, Prater will not be eligible for reinstatement until Week 6 against the New York Jets.
ESPN NFL Insider Adam Schefter and ESPN.com Broncos reporter Jeff Legwold contributed to this report.