In the latest turn in the scandal, known as "Deflategate," Goodell said he affirmed the suspension in part because of the new revelation that Brady made "a deliberate effort" to keep investigators from reading text messages stored on the device.
The four-time Super Bowl champion directed an assistant to destroy the cell phone on March 6. That was the same day he was due to meet with Ted Wells, an investigator hired by the league to examine allegations that Brady was complicit in a plan to tamper with the balls. The new information emerged during Brady's 10-hour appeal hearing at the NFL's New York headquarters on June 23.
"Rather than simply failing to cooperate, Mr. Brady made a deliberate effort to ensure that investigators would never have access to information that he had been asked to produce," Goodell wrote in his 20-page ruling.
Brady's willful obstruction was more evidence in support of the investigation's finding that Brady participated in a scheme, Goodell said, adding that the episode had compromised public confidence in professional football.
The flap is the latest in a series of scandals that have roiled the NFL over the past year. The league, the most lucrative U.S. sports enterprise, has been harshly criticized for light sanctions it imposed on players involved in incidents of domestic violence. A recent agreement with retired players over concussions could end up costing the NFL $1 billion.
Lawyers for Brady, one of the National Football League's highest-paid players, said he plans to take the case to federal court to overturn to the suspension. And the NFL's players union said in a statement it would "appeal this outrageous decision."
"The commissioner's decision is deeply disappointing but not surprising because the appeal process was thoroughly lacking in procedural fairness," Brady's agent, Don Yee, said in a statement. "Most importantly, neither Tom nor the Patriots did anything wrong. And the NFL has no evidence that anything inappropriate occurred."
In a lawsuit filed minutes after the league announced that the suspension had been upheld, the NFL asked a federal judge in New York to confirm that the suspension was permitted under the league's collective bargaining agreement.
The Patriots said they were "extremely disappointed" in the ruling, adding that "the penalties levied originally were excessive and unprecedented, especially in light of the fact that the league has no hard evidence of wrongdoing."
"It is incomprehensible as to why the league is attempting to destroy the reputation of one of its greatest players and representatives," the team said in a statement.
Goodell initially imposed the suspension in May, after Wells delivered a 243-page report that said the quarterback was probably party to a plan to deflate the footballs below league standards, making them easier to grip.
Brady has denied any knowledge of a plan, which was carried out by two Patriots employees, according to Wells.
EASIER TO GRIP
The under-inflated footballs were used by the Patriots in the AFC title game in January, when New England handily beat the Indianapolis Colts 45-7.
Wells said text messages between the two employees implicated Brady in the plan, and while the quarterback said he was not involved in the plot, he refused to relinquish his phone to investigators, citing privacy concerns.
Goodell on Tuesday said that Brady had in fact destroyed the phone, along with some 10,000 text messages stored on it.
Representatives for Brady said during the appeal that the quarterback periodically obtains a new phone and gives his old device to assistants to destroy for security reasons. But the NFL said Brady did not explain why he began using a new phone the day he met with investigators.
The four-game suspension handed to Brady for the upcoming season was meted out by the NFL's vice president of football operations, Troy Vincent, and approved by Goodell.
Goodell himself decided to hear the appeal, a move that has been derided by the NFL Players Association but within his rights as defined by the labor agreement.
Goodell also fined the Patriots $1 million for the team's role in the "Deflategate" scandal, and ordered it to surrender two draft choices, including the team's coveted No. 1 pick in 2016.
Patriots owner Robert Kraft, one of Goodell's biggest supporters, denied the team had any role in the scandal but decided not to appeal the penalty, saying the league must turn the chapter on the ordeal.
After beating the Colts in the AFC championship, the Patriots edged the Seattle Seahawks 28-24 in the Super Bowl.
Scandal is not new to the Patriots, having been found in 2007 of illegally taping opposing coaches.
The league fined the Patriots $250,000, head coach Bill Belichick $500,000, and docked the team a first-round selection in the 2008 NFL Draft.