The Liverpool striker had been given two days to decide whether to appeal against the sanction imposed after the incident during the 2-2 draw at Anfield on Sunday but has not done so.
It means the Uruguay international will miss Liverpool's last four games of this season and, if he is still at the club, the next six domestic games of next season - potentially leaving him sidelined until the start of October.
The FA said in a statement: "Liverpool forward Luis Suarez has not appealed the suspension issued to him by an independent regulatory commission this week.
"A three-person independent regulatory commission upheld the FA's claim that a suspension of three matches was clearly insufficient and the player will now serve a further seven first-team matches in addition to the standard three.
"The suspension begins with immediate effect and applies to Liverpool FC's next 10 domestic first-team fixtures. The FA intends to publicise the independent regulatory commission's written reasons in due course."
After consideration with legal representatives, Suarez decided to accept the punishment and issued another apology for his actions via his Twitter account.
"I acknowledge that my actions were not acceptable on the football pitch so I do not want to give the wrong impression to people by making an appeal," he wrote.
Managing director Ian Ayre said: "The charges against Luis were his to consider and we have to respect his decision to not appeal the 10-game ban.
"We are all disappointed at the severity of the punishment and in particular the differing standards that have been applied across various previous incidents. Luis is an important member of our team and nothing has changed in that regard.
"We are committed to helping him improve his conduct and he will be given our full support. We look forward to him returning to the team next season when he is available for selection."
Brendan Rodgers added: "We can't hide our disappointment at the outcome of this situation, but we have to move on and support Luis in his decision. Luis has made a huge contribution to the squad this season and we respect his decision to accept the ban.
"He will be missed for the remainder of this season and the early part of next, but we will have the opportunity to welcome a better person and player when he returns."
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