Brady's agent blasted the punishment and promised to appeal the decision.
The Patriots were also fined $1 million and will forfeit its first-round selection in the 2016 NFL Draft and fourth-round pick in the 2017 draft, the league announced Monday.
The investigation was initiated to determine what was behind the Patriots' use of underinflated footballs during January's AFC championship game against the Indianapolis Colts. The Patriots beat the Colts en route to a Super Bowl XLIX victory.
The Wells report found that
"it is more probable than not" that Brady was "at least generally aware of the inappropriate activities" of locker room attendant Jim McNally and equipment assistant John Jastremski.
Jastremski has been with the team for 14 years, the past three as the staffer in charge of preparation of the game-day footballs.
In a letter to Brady, NFL Executive President Troy Vincent said the quarterbacks actions were detrimental to the integrity of the sport.
"Each player, no matter how accomplished and otherwise respected, has an obligation to comply with the rules and must be held accountable for his actions when those rules are violated and the public's confidence in the game is called into question," Vincent wrote,
The 243-page Wells report said
Brady, who answered questions from investigators over the course of one day, did not turn over personal information such as texts and emails. Furthermore, the report doubted the quarterback's claim that he didn't know the name of McNally, the part-time Patriots employee who investigators think most likely improperly deflated footballs just before the team faced off in January's AFC championship game.
Brady will be suspended for the first four regular season games of 2015, but can participate in training camp and other activities including preseason games.
Jastremski and McNally, who have been indefinitely suspended without pay since May 6, cannot be reinstated without NFL approval, the league said.
In the event the two staff members are reinstated, they will be prohibited from certain duties, such as managing the locker room or overseeing preparation of the game footballs.
NFL Commissioner Roger Goodell said the punishment is in line with the findings of the Wells report.
"We relied on the critical importance of protecting the integrity of the game and the thoroughness and independence of the Wells report," he said.
In announcing the penalties, the NFL also noted that the report did not find evidence of wrongdoing on the part of the coaching staff.
Reaction was swift on social media, from fans, sportswriters and celebrities alike.
Goodell was a popular target -- some felt that his punishment for the Patriots was too harsh, and compared it to his original punishment for Ray Rice, who was suspended for two games after a domestic violence incident before a video surfaced and cost him his career.
Brady's agent, Don Yee, said "the discipline is ridiculous and has no legitimate basis."
"In my opinion, this outcome was predetermined; there was no fairness in the Wells investigation whatsoever," Yee said in a statement. "There is no evidence that Tom directed footballs be set at pressures below the allowable limits."
Yee asserted that if an appeal is heard by a neutral party, the Wells report "will be exposed as an incredibly frail exercise in fact-finding and logic."
The official response from the Patriots organization was that they continue to deny tampering with the balls, but were willing to face any discipline handed down. But the team and Chairman and CEO Robert Kraft said the sanctions announced by the NFL "far exceeded any reasonable expectation."
The Patriots called the investigation one-sided and stood by their quarterback
"Tom Brady has our unconditional support. Our belief in him has not wavered," the team said.
The legacy of the the Superbowl-winning quarterback might hang in the final outcome of an appeal.
"I think this will be in the first or second paragraph of any bio that's ever written about Tom Brady going forward," CNN Sports analyst Christine Brennan said. "This is absolutely a huge hit to Brady's reputation as Mr. Clean, as the boy next door -- the smiling, laughing guy that everyone seemed to like."
But Brady is not short on defenders
, who say the Wells report was inconclusive.
The document contains a lot of information, but also a lot of words like "probable" and "generally."
In the report, no one said the quarterback tampered with the balls himself. The evidence implicating him comes from texts involving and interviews with McNally and Jastremski.
The NFL took into account that Brady declined to turn over texts and other evidence to investigators.
Brady's agent, Don Yee, told CNN's Anderson Cooper that the quarterback didn't agree to hand over text messages because that would set a bad precedent for other players involved in disciplinary investigations.