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.
More top news
The widow of an Islamic State leader has been charged with conspiracy in the death of US hostage Kayla Mueller.
David Cameron's mother has apparently signed a petition against spending cuts in his constituency.
Terry Wogan was turned down for a job at the BBC by Sir David Attenborough in 1965, recently unearthed letters reveal.