The 28-year-old forward replaces Nick Foligno, who was traded last season. Jenner had been an alternate captain since 2015-16.
"I'm very excited to wear the 'C' for the guys in the room," Jenner said. "It doesn't change anything for me or the way I approach my teammates. I know it's a bigger role and a bigger step but I know that I want to stay true to myself."
Jenner is entering his ninth NHL season with the Blue Jackets, who selected him in the second round (No. 37) of the 2011 NHL Draft. He signed a four-year, $15 million contract ($3.75 million average annual value) July 28 after scoring 17 points (eight goals, nine assists) in 41 games last season, averaging 18:00 minutes of ice time and leading Columbus in face-off winning percentage (55.1 percent). He has scored 240 points (121 goals, 119 assists) in 530 regular-season games and 15 points (eight goals, seven assists) in 37 Stanley Cup Playoff games.
"Boone was the obvious choice," coach Brad Larsen said. "There's no question about it. There's a lot of layers when naming a captain and Boone checked all the boxes.
"He embodies who the Columbus Blue Jackets are."
Defenseman Zach Werenski and forwards Oliver Bjorkstrand and Gustav Nyquist were each named an alternate captain. Werenski signed a six-year, $57.5 million contract extension ($9.58 million average annual value) July 29 that begins next season.
"All three are so deserving," Jenner said. "I've seen [Bjorkstrand and Werenski] since they came in and seen their growth every year."
Jenner is the seventh captain in Blue Jackets history, joining Foligno (2015-21), Rick Nash (2008-12), Adam Foote (2005-08), Luke Richardson (2003-05), Ray Whitney (2002-03) and Lyle Odelein (2000-02).
The Blue Jackets open the regular season against the Arizona Coyotes on Thursday (7 p.m. ET; BSOH, BSAZ, ESPN+, NHL LIVE).
Five NHL teams do not have a captain: the Arizona Coyotes, Buffalo Sabres, Calgary Flames, New York Rangers and Ottawa Senators. The expansion Seattle Kraken named defenseman Mark Giordano their first captain Monday.
The Montreal Canadiens likely won't have a captain on the ice this season after general manager Marc Bergevin said Sept. 6 that a replacement will not be named for defenseman Shea Weber, who is expected to be out for the season. Center Jack Eichel was stripped of Buffalo's captaincy Sept. 23 after he failed his physical at training camp and was placed on injured reserve.
NHL.com independent correspondent Craig Merz contributed to this report