The president, who has a home in Chicago, is a diehard Chicago White Sox fan but rooted for the Cubs after the Sox failed to reach the postseason.
The Cubs won their first World Series title since 1908 by defeating the Cleveland Indians in November.
As Obama walked into the East Room, the boisterous audience chanted, "Let's Go, Cubbies!"
"They said this day would never come," Obama said as he started his remarks, adding: "Something none of my predecessors ever had a chance to say, 'Welcome to the White House, the World Series champion Chicago Cubs.' ... I will say that the Cubs took long enough. I've only got four days left."
Cubs first baseman Anthony Rizzo, who wears No. 44, presented the nation's 44th president with a No. 44 Cubs jersey with OBAMA on the back.
"Among Sox fans," Obama said, "I'm the Cubs' No. 1 fan."
Cubs president Theo Epstein issued a "midnight pardon" to the president for being a White Sox fan.
Obama said on Martin Luther King Day that "sports has the power to bring us together even when we're divided. There is a line between Jackie Robinson and me standing here. Sports has a way sometimes of changing hearts in a way that politics or business hasn't."