Michael Adebolajo, 29, and Michael Adebowale, 22 have been convicted of killing the 25-year-old soldier Lee Rigby after they ran him over and hacked him to death near his barracks in Woolwich, South London.
Fusilier Rigby's family said they were satisfied that justice had been done.
In a statement read by Detective Inspector Pete Sparks, they said: "No one should have to go through what we have been through as a family.
"We are satisfied that justice has been done, but unfortunately no amount of justice will bring Lee back.
"These people have taken him away from us forever but his memory lives on in all of us and we will never forget him.
"We are very proud of Lee, who served his country, and we will now focus on building a future for his son Jack, making him as proud of Lee as we all are.
"Lee will be sorely missed by his siblings, nieces, nephew and all of those who loved him.
"We now ask that we are left alone to grieve through our loss."
Sources: ITN/PA
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