The jury took four and a half hours to reach the two unanimous guilty verdicts.
As the guilty verdict was read out on the murder charge, there were gasps from the public gallery and some of Rigby's relatives left the court in tears.
Rigby, dressed in a grey suit, shirt and tie, put his head in his hands as the verdict was given.
Smedley, dressed all in black and with her dark hair tied back, appeared to be struggling to hold back tears when the jury announced her guilty verdict.
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A man who met PC Keith Palmer said his murder "sent a shiver down my spine".
Brothers Jayden and Carlos Cortez, aged 1 and 2, were in their babysitter's car when it was stolen in California.
Officers said the girls were approached during separate incidents earlier this week in south London - possibly by the same suspect.