The reigning Super Bowl MVP announced the name on his Twitter account Wednesday, one day after the baby was born, saying: "Brit finally gave in."
Earlier this month, Brees posted a Twitter message soliciting ideas for uncommon boy names that begin with the letter "B." Brees said within days he had received more than 6,000 responses.
"It wasn't really a name battle, but it was," Brees told The Times-Picayune. "We had a lot of good choices, and Bowen has been mine ever since Baylen was born. ... I always hoped we'd be able to give him a little brother."
The Associated Press contributed to this report.