Bryant received 29 of a possible 30 first-place votes.
Washington Nationals second baseman Daniel Murphy was the runner-up. Los Angeles Dodgers shortstop Corey Seager was third after he was the unanimous winner of the NL Rookie of the Year award on Monday.
Bryant was arguably the best offensive player on the best team in the game and showed exceptional defensive versatility by playing in both the infield and the outfield.
Bryant hit .292 with 39 homers and 102 RBIs in just his second year in the majors, helping the Cubs to their first World Series title since 1908.
Bryant led the National League with a 7.67 WAR and was the only NL player in the top 10 in that category. He also ranked third in the NL in home runs (39), fourth in OPS (.939) and sixth in RBIs (102).
The 2015 NL Rookie of the Year, Bryant also led the league in runs scored with 121.
"Kris is just an impressive young man in every aspect,'' Cubs owner Tom Ricketts said. "[He] is very mature, professional, light-hearted, but serious at the same time. He's just kind of a dream player for any organization.''
He also is the first player ever to win college player of the year, minor league player of the year, rookie of the year and MVP in four straight seasons.
Balloting was done by the Baseball Writers Association of America at the start the playoffs. The BBWAA began voting for the award in 1931.
Bryant becomes the Cubs' first MVP since Sammy Sosa won the award in 1998. The Las Vegas native joins Andre Dawson (1987), Ryne Sandberg (1984), Ernie Banks (two times, 1958 and 1959), Hank Sauer (1952), Phil Cavarretta (1945) and Gabby Hartnett (1935) as BBWAA winners.
He becomes just the sixth player to win rookie of the year and MVP in one or consecutive seasons.
Bryant was the unanimous NL Rookie of the Year after he hit .275 with 26 homers and 99 RBIs last season. Bryant joins Dustin Pedroia (2007-08), Ryan Howard (2005-06) and Cal Ripken (1982-83) as the only players to go Rookie of the Year-MVP in consecutive seasons. Ichiro Suzuki (2001) and Fred Lynn (1975) are the only players to win the awards in the same year.
Information from The Associated Press and ESPN's Jesse Rogers contributed to this report.