The NFL began investigating after the Patriots defeated the Colts 45-7 on January 18. The Colts complained that several footballs were under-inflated and the NFL confirmed that 11 of the 12 footballs were under the limit. The investigation started as the Patriots were preparing for the Super Bowl - which they won two weeks later.
Footballs with less pressure can be easier to grip and catch. Some quarterbacks prefer footballs that have less air.
The NFL requires balls to be inflated between 12.5 and 13.5 pounds per square inch, and each team is responsible for the balls it uses on offense.
Brady said he prefers footballs inflated to 12.5 pounds per square inch. On many occasions, Brady said he never asked for balls to be deflated outside of the rules.
The NFL report said "it was more than probable than not" that Jim McNally, the officials' locker room attendant, and John Jastremski, an equipment assistant for the Patriots, were involved in "a deliberate effort to release air" from the footballs after they were examined by the referee.
The report includes text messages between McNally and Jastremski - sent in October and January - that imply Brady was requesting footballs deflated below 12.5 pounds per square inch. They described requests from McNally for shoes and signed footballs from Brady in exchange for deflating the balls.
The texts imply that Brady had previously been upset with the quality of the game balls.
"Remember to put a couple sweet pig skins ready for tom to sign," one said.
"Nice throw in some kicks and make it real special," another said.
NFL Commissioner Roger Goodell said the league would consider what steps to take next.
"We will continue our efforts vigorously to protect the integrity of the game and promote fair play at all times," he said.
The 243-page report said league investigators found no evidence that coach Bill Belichick and team management knew of the practice. Owner Robert Kraft, who strongly defended his team and said the NFL would owe the Patriots an apology if the investigation turned up no culpable evidence, said he still doesn't believe the team did anything wrong.
"While I respect the independent process of the investigation, the time, effort and resources expended to reach this conclusion are incomprehensible to me,'" Kraft said.
But, he said the Patriots would accept the findings of the report "and take the appropriate actions based on those findings as well as any discipline levied by the league."