He has long been expected to run. Brown has flirted with a bid for months, moving from Massachusetts last year. He has been on a month-long "listening tour" in which he's publicly discussed a challenge to Shaheen, and said last week that he would definitely run against her.
Shaheen has led in most public polls by a high-single-digit margin.
WMUR first reported the news of Brown's decision.
—This post was updated at 9:08 a.m.
Alexandra Jaffe contributed to this report.