Megan, from Stirling, was at the event to perform the official Poppy Appeal song ‘The Call (No Need To Say Goodbye)” with group The Poppy Girls.
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The group consists of five servicemen’s daughters aged 10 to 17 who were chosen following a talent search within the Armed Forces community.
Huw Edwards announced the surprise while the girls were on stage, in front of an audience including the Queen, Prince Phillip and David Cameron.
Megan rushed towards her father as he walked through an applauding audience and was embraced in an emotional hug.
Billy is normally based 80 miles from home in Rosyth, Dunfermline but for the last few months has been in the Seychelles with the Navy as part of an anti-piracy force targeting Somali pirates. He was not due back in the UK until January.
Billy will be flying back to the Seychelles on Wednesday allowing the family a couple of days together before spending Christmas apart.
The Festival of Remembrance, held the Saturday before Remembrance Sunday, is a yearly event that pays tribute to members of the Armed Forces who have given their lives.
The long running festival is held at the Royal Albert Hall and audience members include members of the royal family, military and government members.