The Ricketts family will buy 95% of the National League Cubs, its Wrigley Field ball park and Tribune's approximately 25% interest in Comcast SportsNet. The family is ranked 161 in the Forbes list of the wealthiest Americans, with a net worth of $2.6bn.
Troubled newspaper group Tribune, which went into chapter 11 bankruptcy protection in December, will retain a 5% interest.
Joe Ricketts, founder, former CEO and former chairman of broker TD Ameritrade, said: "Our family is thrilled to have reached an agreement to acquire a controlling interest in the Chicago Cubs, one of the most storied franchises in sports.
"The Cubs have the greatest fans in the world, and we count our family among them. We look forward to closing the transaction so that we can begin leading the Cubs to a World Series title."
The Ricketts family reached the agreement with Tribune, which also owns the Chicago Tribune, after a bid process that began more than two years ago when real estate billionaire Sam Zell bought Tribune for $8.2bn (£5bn).
It is understood that the Ricketts family fought off competition from Marc Utay, a New York investment banker, and Leo Hindery, a media investor who formerly headed the Yankees Entertainment and Sports Network.
According to a report in the New York Times, Utay offered $40m less cash than the Ricketts family, and though overall his bid was worth $100m more, Tribune's investors wanted cash because of the company's debts.
Zell, the chairman of Tribune, said: "This joint venture will provide dedicated, local family ownership and management for the team. The Ricketts family will be a great steward of the franchise. They have a strong respect for the team, for the fans and for what the Cubs mean to the City of Chicago."
Final approval of the deal is dependent upon approval by Major League Baseball owners and the bankruptcy court.
As part of the court's approval process, the entity holding most of the assets of the Cubs franchise will voluntarily file for Chapter 11 protection so that the franchise can emerge free and clear of Tribune Company's financial obligations.
All obligations specific to the Cubs franchise - player contracts and agreements with sponsors, broadcasters, advertisers, suppliers and ticket holders - are not expected to be impacted by the court approval process, and there should be no interruption of team operations.
Chicago Cubs fans will be hoping that Joe Ricketts is as good as his word and that new ownership will help the club win its first World Series since 1908.
However, it is unlikely to be this year. The Cubs might be second in the National League Central behind the St Louis Cardinals, but they are ten games behind. This puts them fifth in the wild card and unlikely to make the post season.
The New York Times is the only other newspaper group that still has an interest in a baseball club. It owns a 17.5% stake in New England Sports Ventures, which owns the Boston Red Sox.