The penalty leaves the London club on -26 points in the early Gallagher Premiership table.
A statement from Premiership Rugby announced: "The sanction that has been imposed on Saracens Rugby Club by the panel is a total fine of £5,360,272.31 and a total deduction of 35 league points."
The alleged breaches spanned the last three seasons but the points deduction will be applied in full this season.
The Premiership Rugby statement added: "The decision of the independent panel is that Saracens Rugby Club failed to disclose payments to players in each of the seasons 2016-17, 2017-18 and 2018-19.
"In addition, the club is found to have exceeded the ceiling for payments to senior players in each of the three seasons. The panel therefore upheld all of the charges.
"The salary cap regulations stipulate that a points deduction may be imposed in the current season (2019-20) only. The sanction has no bearing on any other domestic or European competition."
Saracens have won back-to-back Premiership titles and are reigning European champions, but this decision is a hammer blow to the team both on a sporting and financial level.
England stars Owen Farrell and Billy Vunipola are just two of the big names on the club's roster.
The club have the right to have the case reviewed but must prove an error of law, that the decision is irrational or that there has been some procedural unfairness, the Premiership Rugby statement said. If the club seeks a review, the sanctions will be suspended.
A Premiership Rugby spokesperson said: "The salary cap is an important mechanism to ensure a level playing field for Premiership clubs and maintain a competitive, growing and financially sustainable league.
"Today's decision by the independent panel upholds both the principle of the salary cap and the charges brought following an extensive investigation by Premiership Rugby.
"We are pleased that this process has reached a conclusion and we look forward to another exciting season of Premiership Rugby."